Unit A: Geometry

Chapter 1: Polygons

Practice

Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.

Practice
Solutions

1.

The lamp is in the shape of an isosceles trapezoid. AB = 5 cm, BC = 7 cm, CD = 10 cm, and

∠ D = 55 °

. Find the length of AD and angle measure of

∠ D

.

1.

The lamp is in the shape of an isosceles trapezoid. AB = 5 cm, BC = 7 cm, CD = 10 cm, and

∠ D = 55 °

. Find the length of AD and angle measure of

∠ D

.

In an isosceles trapezoid, the two opposite, non-parallel lines are the same length and the two other sides are parallel. As a result,

∠ C = ∠ D = 55 °

and

∠ A = ∠ B

. The interior angles in a quadrilateral add up to 360°, so

\begin{array}{rcl} ∠ A + ∠ B + ∠ C + ∠ D & = & 360 ° \\ ∠ A + ∠ A + 55 ° + 55 ° & = & 360 ° \\ 2 ∠ A + 110 ° & = & 360 ° \\ 2 ∠ A & = & 250 ° \\ ∠ A & = & \frac{250 °}{2} \\ ∠ A & = & 125 ° \end{array}