Question

Determine the value of x and find measure of both angles

Answer 1

Given:

m∠1 = 20 - 8x

m∠2 = 30 - 16x

From the image we can see that m∠1 and m∠2 are corresponding angles, and corresponding angles are equal.

Therefore, we have:

m∠1 = m∠2

20 - 8x = 30 - 16x

Let's solve for x:

Add 16x to both sides:

20 - 8x + 16x = 30 - 16x + 16x

20 + 8x = 30

Subtract 20 from both sides:

20 - 20 + 8x = 30 - 20

8x = 10

Divide both sides by 8:

`\begin{gathered} (8x)/(8)=(10)/(8) \\ \\ x\text{ = }1.25 \end{gathered}`

x = 1.25

m∠1 = 20 - 8x = 20 - 8(1.25) = 20 - 10 = 10

m∠1 = 10

m∠2 = 30 - 16x = 30 - 16(1.25) = 30 - 20 = 10

m∠2 = 10

ANSWER:

x = 1.25

m∠1 = 10 degrees

m∠2 = 10 degrees