Question

identify the relationship between ∠1 and ∠2. 130. 131. 132. 133. find the value of x. 134. 135. 136. 137. 138. 139.

Explanation:

130.

The two lines are perpendicular, so $\angle1$ and $\angle2$ are vertical - angles. Vertical angles are equal.

131.

$\angle1$ and $\angle2$ are adjacent angles. They share a common side and a common vertex.

132.

$\angle1$ and $\angle2$ are adjacent angles. They share a common side and a common vertex.

133.

$\angle1$ and $\angle2$ are complementary angles since the angle formed by the two lines is a right - angle ($90^{\circ}$) and $\angle1+\angle2 = 90^{\circ}$.

134.

The two angles are supplementary (a straight - line is $180^{\circ}$). So $x=180 - 48=132^{\circ}$.

135.

The two angles are complementary (the angle is a right - angle, $90^{\circ}$). So $x = 90-54 = 36^{\circ}$.

136.

The two angles are vertical angles. Vertical angles are equal. So $x = 123^{\circ}$.

137.

The two angles are complementary (the angle is a right - angle, $90^{\circ}$). So $x=90 - 60=30^{\circ}$.

138.

The two angles are vertical angles. Vertical angles are equal. So $x = 85^{\circ}$.

139.

The two angles are vertical angles. Vertical angles are equal. So $x = 27^{\circ}$.

Answer:

1. Vertical angles.
2. Adjacent angles.
3. Adjacent angles.
4. Complementary angles.
5. $x = 132^{\circ}$
6. $x = 36^{\circ}$
7. $x = 123^{\circ}$
8. $x = 30^{\circ}$
9. $x = 85^{\circ}$
10. $x = 27^{\circ}$