Answer:
- m∠1 = 13°
- m∠2 = 77°
- m∠3 = 90°
Explanation:
Vertically opposite angles: Vertically opposite angles are two angles that are formed opposite each other when two lines intersect. Vertically opposite angles are always equal to each other.
In this case:
m∠2 and 77° are vertically opposite angles.
So,
m∠2 = 77°
and
m∠3 and 90° are vertically opposite angles.
So,
m∠3 = 90°
Linear pair: A linear pair is a pair of adjacent angles that form a straight line. The sum of the measures of the two angles in a linear pair is always 180 degrees.
In this case:
m∠1, m∠2 and 90° are linear pair.
So,
m∠1 + m∠2 + 90° = 180°
Substitute value:
m∠1 + 77° + 90° = 180°
m∠1 + 167° = 180°
Subtract 167° on both sides:
m∠1 + 167° - 167° = 180° - 167°
m∠1 = 13°
Therefore, answer is:
- m∠1 = 13°
- m∠2 = 77°
- m∠3 = 90°