Question

for problems 11 - 13, state whether the angles are supplementary or complementary. then find the missing angles. 11) ∠pae is straight 12) ∠adc is right 13) ∠wxy is right

Explanation:

Step1: Recall angle - sum properties

Complementary angles sum to 90°, supplementary angles sum to 180°.

Step2: Solve problem 11

Since $\angle PQR$ is straight ($180^{\circ}$), the angles are supplementary. Let the missing angle be $x$. Then $x + 50^{\circ}=180^{\circ}$, so $x=180^{\circ}- 50^{\circ}=130^{\circ}$.

Step3: Solve problem 12

Since $\angle ADC$ is right ($90^{\circ}$), the angles are complementary. Let the missing angle be $y$. Then $y + 58^{\circ}=90^{\circ}$, so $y=90^{\circ}-58^{\circ}=32^{\circ}$.

Step4: Solve problem 13

Since $\angle WXY$ is right ($90^{\circ}$), the angles are complementary. Let the missing angle be $z$. Then $z + 65^{\circ}=90^{\circ}$, so $z=90^{\circ}-65^{\circ}=25^{\circ}$.

Answer:

1. Supplementary, missing angle is $130^{\circ}$.
2. Complementary, missing angle is $32^{\circ}$.
3. Complementary, missing angle is $25^{\circ}$.