WORKING WITH ANGLE MEASURES

**Vertical angles** are the opposite angles formed by the intersection of two lines, line segments, and/or rays. In the image [*right*], angles 1 and 4 are vertical angles, and angles 2 and 3 are vertical angles. Vertical angles have the same measure. | |

A **linear pair** is two adjacent angles which form a straight angle. The sum of the two angle measures is 180°. In the image [*right*], angles 1 and 2 form a linear pair. | |

**Supplementary angles** are two angles whose measures sum to 180°.

**Complementary angles** are two angles whose measures sum to 90°.

Since triangle ABC is an equilateral triangle, angle 1 is 60°.

Angles 1 and 3 are vertical angles.

Vertical angles have the same measure.

So, the measure of angle 3 is 60°.

Angles 1 and 2 are adjacent angles which form a straight angle.

So, the sum of the measures of angles 1 and 2 is 180°.

Set up an equation and solve for the measure of angle 2.

measure of angle 1 + measure of angle 2 | = | 180° |

60° + measure of angle 2 | = | 180° |

measure of angle 2 | = | 180° − 60° |

measure of angle 2 | = | 120° |

So, the measure of angle 2 is 120°.