Question

1. determine the measure of all the angles in each diagram. a. b. (x - 20)° 100° 4x° 36°

Explanation:

Step1: Use corresponding - angle property for part a

Since the two lines are parallel, the corresponding angles are equal. So, $4x = 36$.

Step2: Solve for $x$ in part a

Divide both sides of the equation $4x = 36$ by 4. We get $x=\frac{36}{4}=9$.
The angles are $36^{\circ}$ and its corresponding angles (equal to $36^{\circ}$), and the supplementary angles which are $180 - 36=144^{\circ}$.

Step3: Use vertical - angle property for part b

Vertical angles are equal. So, $x - 20=100$.

Step4: Solve for $x$ in part b

Add 20 to both sides of the equation $x - 20=100$. We get $x = 100+20=120$.
The angles are $100^{\circ}$ and its vertical - angle (equal to $100^{\circ}$), and the supplementary angles which are $180 - 100 = 80^{\circ}$.

Answer:

In part a: The angles are $36^{\circ},144^{\circ},36^{\circ},144^{\circ}$. In part b: The angles are $100^{\circ},80^{\circ},100^{\circ},80^{\circ}$.