Angle Basics and Measurements Geometry Angles and Intersecting Lines Angle Basics and Measurements Questions What is the diameter of a circle if its circumference is 25.8 inches? How do you find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third angle measures 3 times the second angle decreased by 12? How can angles be adjacent? How are adjacent angles used in real life? How do you identify vertical angles? What are some examples of adjacent angles? How do you describe an acute angle? How do you bisect an acute angle? How do you find the related acute angle? How do you find the positive acute angle? Why can two acute angles be supplementary? How big can an obtuse angle be? How do you bisect an obtuse angle? How many degrees does an obtuse angle have? What is the value of #x# in a triangle with angles #70, 60#, and #8x + 2#? What is 1/3 of a right angle? Why can't a triangle have a right angle and an obtuse angle? Does no trapeziod contain a right angle? How many times does a clock make a right angle? What is a rhombus with right angles? How many right angles does a right triangle have? In a right triangle, is the side opposite the right angle the shortest side? If a parallelogram has a right angle, is it a rectangle? How many degrees are in a right angle? What shapes have 4 right angles? What is the difference between a right angle and a straight angle? Does every parallelogram have at least one right angle? For a right triangle ABC with right angle C, if AC = 4 and AB = 5, what is the length of BC in simplified form? If ABC is a right triangle and angle A=45°, what degrees are B and C? How many right angles are in an octagon? Is it possible to have a equilateral right triangle? What does a rhombus with two right angles look like? Can a Triangle have 1 right angle and 3 equal sides? Are all right angles congruent? What is a right angle, acute angle, and obtuse angle? Can I make a hexagon with 3 right angles? How many right angles are in a regular pentagon? How do you calculate the area of a triangle without a right angle? How many right angles can a triangle contain? How many right angles does a hexagon have? How many right angles does a rectangle have? How many right angles does a rhombus have? How many right angles does a trapezoid have? In a right triangle, if #a=3# and #b=6#, what is the value of #c#? The hypotenuse is 6, and one of the leg is 4. How do you find the missing leg length? Question #aff5e Question #5ec05 What is 20 divided by 2/9? A right-angled triangle has an angle of #28^circ# and a hypotenuse of #8# cm. What are the lengths of the other two sides? Question #672c6 ABC is an acute angled triangle. The bisector of #/_# BAC intersects BC at D. BE is a perpendicular drawn on AC from B. Points E and D are joined. Show that #/_CED>45^o# How to show? Let #hat(ABC)# be any triangle, stretch #bar(AC)# to D such that #bar(CD)≅bar(CB)#; stretch also #bar(CB)# into E such that bar(CE)≅bar(CA). Segments #bar(DE) and bar(AB)# meet at F. Show that #hat(DFB# is isosceles? A triangle #hat(ABC)# has vertices of #A(1,3);B(1/2,3/2);C(2,1)#. Verify that the triangle is isosceles and calculate the area and perimeter? A composite geometrical shape is made up of a square, equilateral and right triangles. Calculate the area of hatched triangle? For the composite geometric shapes given the semi circle has the same area measure as the right angle triangle, and the base of right triangle is congruent to the radius of the semicircle. Calculate the value of angle #theta#? Give a composite shape of quarter of circle and rectangle with a total area of #570 " square feet"# and and the diagonal angle of the rectangle equal to #18.43^0#, calculate the radius? Given the right trapezoid calculate angle #theta# and the area of triangle #hat(EAD)#, provided #EA=4, AB=BC=CD=DA=2, AB_|_EC#? A composite geometric shape of triangle and rectangle is given with the proportionate relation given in the figure. Find angle #alpha# and #theta#? Question #63619 Question #ec325 Calculate x, y, Perimeter and area of the composite geometrical figure? How do we find the eccentric angle of ellipse #x^2/16+y^2/4=1#? Payton colored a composite shape made up semicircles whose diameters are the sides of a square. The result is a shape given below. Find the area of the shaded region (Petals) in terms of x? Calculate the area using the dimension in 2nd figure? Consider any triangle (see figure). Define #sin theta = h/c#, show that the area of triangle is #A_Delta = 1/2 (b*c) sintheta# where #b and c# are any two sides of the traingle that make the angle #theta#? A composite geometry is made up of cube and a square pyramid frustum. The slanted side AK stretch a side lengths of 5.62 forming an isosceles triangle. Calculate the volume, surface area and sketch the net of the surface area? From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is #57°#, as shown below. If the distance between the radio antenna and the library is #1.3 mls#, how many miles high is the balloon? The diameter for the smaller semicircle is #2r#, find the expression for the shaded area? Now let the diameter of the larger semicircle be 5 calculate the area of the shaded area? Question #ef7d5 How do you find the angle measure of the missing angle for a quadrilateral with angle measures of 145 degrees, 85 degrees and 45 degrees? In #DeltaABC,/_BAC=30^@;/_ACB=60^@ and BC = 6 cm#. How will you find out the area of the triangle without using trigonometry? In the #DeltaABC# below, #M# and #N# are midpoints of #BC# and #AB# respectively, #m/_A=90^@#. Find #x,y# and #z#? Draw an angle ∠ABC. Find the bisector of this angle? What is the value of x? Let #bar(AB)# be cut into equal and unequal segments at #C and D# Show that the rectangle contained by #bar(AD)xxDB# together with the square on #CD# is equal to the square on #CB#? Start with #DeltaOAU#, with #bar(OA) = a# , extend #bar(OU)# in such a way that #bar(UB) = b#, with #B# on #bar(OU)#. Construct a parallel line to #bar(UA)# intersecting #bar(OA)# at C. Show that, #bar(AC) = ab#? Use a square a mechanism to calculate #sqrt(2)# geometrically? A triangle has angles of #78°#, #47°#, and #x+65°#. What is the value of #x#? Draw the symmetrical shape to the given about the given axis? Five times the complement of an angle less twice the angle's supplement is 450. How do you find the the measure of the supplement? How do you convert the angle to a decimal in degrees 55° 19'8"? Given a square with side #s# calculate the area of the curved square, (purple shade area in the figure to the left)? The 2nd figure is to the right is sketched to help guide your thinking? Question #52a3e Find the area of the shade area plus the middle curved square, regions - 1, 2, 3, 4 and 5? All four circles are equal with radius r? Given that the radius of the circumcircle (large circle) is #r#, evaluate the ratio of the area of A regions to B regions - #(sumA_i)/(sumB_i)#? What do the interior angles of a polygon have to add up to? If the exterior angle in a polygon is 12 degrees what is the number of sides? Question #8de09 In an triangle, AC = BC and #AC^2 = 2AB^2#, then what will be angle of C? Question #3ff3d Question #a40d8 Given #ABC# a triangle where #bar(AD)# is the median and let the segment line #bar(BE)# which meets #bar(AD)# at #F# and #bar(AC)# at #E#. If we assume that #bar(AE)=bar(EF)#, show that #bar(AC)=bar(BF)#?. How do you write the degree measure over 360 to find the fraction of the circle given #72^circ#? How do you write the degree measure over 360 to find the fraction of the circle given #120^circ#? How do you write the degree measure over 360 to find the fraction of the circle given #36^circ#? How do you write the degree measure over 360 to find the fraction of the circle given #270^circ#? How do you write the degree measure over 360 to find the fraction of the circle given #240^circ#? How do you write the degree measure over 360 to find the fraction of the circle given #45^circ#? ABC is a right angle triangle. AD is drawn perpendicular to BC. If BC = 9cm, BD = 4 cm then find AB? The figure shows △ABC.¯¯BD¯ is the angle bisector of ∠ABC. What is AD ? What is the value of x? How do you find co terminal angles (find one positive, and one negative)? Question #26efe Question #ee245 If angle ABC = angle XYZ what is the mesure of A? Let c= 12, z=18, and x=27 Charlene is trying to find the unknown sides of a right triangle with a 30° acute angle, whose hypotenuse measures #12sqrt2#. What is Charlene's error? Question #366ac What are the proper units for measuring angles? Question #8183c Find the angles of the triangle formed by vectors #vecP=5hati-3hatj+hatk#, #vecQ=-2hati+hatj+5hatk# and #vecR=9hati+5hatj+0hatk#? The measures of the angles of a triangle are in the extended ratio 6:1:5. What is the measure of the largest angle? Question #f5aaf Question #12cb7 Question #e3694 Question #acd05 The sum of two angles, #2x+10# and #3x+15# is 110 degrees. What is the value of #x#? Triangle #XYZ# is and isosceles triangle with a base #/_X=40# degrees. Find the measures of the other base angle and the vertex angle. Please solve? Thanks! Find, in terms of x and y , the equation of the perpendicular bisector of the line segment joining the points(-1,2) and (-7,0) . The equation of the perpendicular bisector is .? The perimeter of a square is at the most 22 feet . Let n represent the length of one side of the sqaure . Write an inequality that represent the situation Of the length 2.5 ft , 4.8 ft, 5.2 ft, 5.8 ft, 6 ft, which could be the side length of the square? Question #2bc16 A right triangle has one angle that measures 15°. What is the measure of the other acute angle? It has a triangle equal to 180 degrees and I don’t understand this, can you help me? The measures of the angles of a triangle are given x + 4 , x , and 2x. what’s the value of x ? Can 4cm and 8cm and 3cm form a triangle? In the diagram below, if OM=8 and MY=9, what does XZ equal? Angles and Intersecting Lines View all chapters Angle Basics and Measurements Angles Between Intersecting and Parallel Lines Complementary and Supplementary Angles Angles with Triangles and Polygons Next