Question

1. ∠dpg and ∠jkl are complementary angles. ∠dpg = x + 4 and ∠jkl = x - 8. find the measure of the two angles.

a. 47&43
b. 45&45
c. 53&37
d. 51&39

1. how are the two angles related?

a. adjacent
b. complementary
c. supplementary
d. vertical

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((x + 4)+(x - 5)=90\).

Step2: Simplify the equation

Combine like terms: \(x+x+4 - 5=90\), which simplifies to \(2x-1 = 90\).

Step3: Solve for \(x\)

Add \(1\) to both sides: \(2x=90 + 1=91\). Then divide by \(2\): \(x=\frac{91}{2}=45.5\).

Step4: Find the measure of \(\angle DPG\)

Substitute \(x = 45.5\) into \(\angle DPG=x + 4\). So, \(\angle DPG=45.5+4 = 49.5^{\circ}\).

Step5: Find the measure of \(\angle JKL\)

Substitute \(x = 45.5\) into \(\angle JKL=x - 5\). So, \(\angle JKL=45.5-5 = 40.5^{\circ}\).

for question 12:
Adjacent angles share a common side and vertex. Complementary angles sum to \(90^{\circ}\), supplementary to \(180^{\circ}\), and vertical angles are opposite each other. Here, \(12^{\circ}+148^{\circ}=160^{\circ}
eq90^{\circ}\), \(12^{\circ}+148^{\circ}
eq180^{\circ}\), and they are not vertical. But they share a common vertex and a non - common side (adjacent).

Answer:

A. \(49.5^{\circ}\) and \(40.5^{\circ}\)