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

-For two intersecting lines, and are a pair of vertical angles formed. Given that m and m , find the value of x.

What is the slope of any line that is perpendicular to the graph of ?

-To the nearest tenth of square inch, find the area of the regular pentagon whose apothem measures 4.2 inches and whose sides measure 6.2 inches.

The point (-1,4) lies in Quadrant IV of the Cartesian coordinate system.

-If is circumscribed about the circle in such a way that m = 90° and m = 110°, which is true?

The driver of an automobile leaves home and travels due east 8 miles. Turning right at an intersection, he drives due south a distance of 6 miles. How far is the driver from home?

-If , then .

In the right triangle ABC with m = 90°, the sides have lengths a = 5, b = 12, and c = 13. Where a is the length of side opposite , find sin .

-How many different lines can be concurrent at point X?

-In , . Which statement is true?

-In the figure, a bird (at point B) is 36 feet above the ground. Meg is 60 feet from the bird while Mara is 39 feet from the bird. How far apart are Meg and Mara?

If two inscribed angles of a circle intercept the same arc, these angles are congruent.

Using a calculator, the value of sin 54° is approximately 0.8090.

How many common tangents do two internally tangent circles have?

For rhombus RSTV, diagonals and intersect at point W. If RT = 16 and VS = 12, find the length of each side of rhombus RSTV.

-To construct an isosceles triangle with vertex angle and legs of length RS:

-If M is the midpoint of , then it can be proved that:

-In a triangle, the lengths of the sides are 9, 12, and 15. What is the length of the radius of the circumcircle?

-If m = 90° and m = 35°, one would use sin A to find the value of b.

For the equation , find in the form an equivalent equation in which the coefficient (multiplier) of x is the number -9.