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.

Find the missing angles in the diagram below.

1.

Find the missing angles in the diagram below.

Step 1: Working with the triangle on the left, find

∠ A

by using your knowledge that the sum of the angles in a triangle is 180°.

\begin{array}{rcl} ∠ A + ∠ B + ∠ C & = & 180 ° \\ ∠ A + 45 ° + 100 ° & = & 180 ° \\ ∠ A + 145 ° & = & 180 ° \\ ∠ A & = & 35 ° \end{array}

Step 2: To find

∠ C

, use the fact that two angles that form a straight line add up to 180°.

\begin{array}{rcl} ∠ A + ∠ B & = & 180 ° \\ ∠ C + 100 ° & = & 180 ° \\ ∠ C & = & 80 ° \end{array}

Step 3: Working with the triangle on the right, find

∠ B

by using your knowledge that the sum of the angles in a triangle is 180°.

\begin{array}{rcl} ∠ A + ∠ B + ∠ C & = & 180 ° \\ 80 ° + ∠ B + 70 ° & = & 180 ° \\ ∠ B + 150 ° & = & 180 ° \\ ∠ B & = & 30 ° \end{array}

The missing angles are

∠ A = 35 °

,

∠ B = 30 °

, and

∠ C = 80 °

.