Exam 12: Geometry Problems: Complementary Angles, Collinear Points, and Similar Triangles

-In , m is 26° larger than m . Find m .

-If m = 57° and m = 123°, then r || s.

Write a simplified form for the positive solution to the equation .

Given that (8,15,17) is a Pythagorean Triple, it follows that (24,45,c) is also a Pythagorean Triple. What is the value of c?

-In isosceles triangle RST, . If , , and the perimeter of is 36, find the value of x.

Two parallel lines l and m are cut by transversal t. For a pair of interior angles on one side of line t, the angle-bisectors are drawn to meet at point E. Find m .

If , then the areas of and are equal.

and intersect at point E. If m and m , find x.

Given that A = (-3,-7) and B = (5,2), find the midpoint of .

For the regular dodecahedron with faces numbered 1, 2, 3, . . . , 12, what is the probability that one roll produces a result for 6 or larger? Provide the answer as a common fraction.

A regular dodecahedron is manufactured as a desk calendar. What is the likelihood that the month facing upward is a month that begins with the letter "J?"

-Given that each edge measures 4 cm, find the total area of the regular tetrahedron.

-Given that , , , and , find PQ.

In a triangle with sides of lengths 6 cm, 7 cm, and 8 cm, find the measure of the angle that is opposite the side of length 8 cm. Give the answer correct to the nearest tenth of a degree.

Square MNPQ is circumscribed about . If the radius of measures 8 cm, find the length of a diagonal of square MNPQ.

-For trapezoid RSTV, , and is the median. If RS = 6.5, ST = 8.5, VT = 14.7, and VR = 9.7, then the length of is:

-For lines l, m, and n to be parallel by pairs, the three lines must be coplanar lines.

-Given that , what angle of is congruent to of ?

Find the value of b so that the points (-1,3), (1,-1), and (3,b) are collinear.

If two angles are supplementary and also congruent, then each of these angles is a(n):