Question

1. find the value of y if cd is parallel to ef and the measure of ∠1 = 4y - 12 and ∠2 = 48°.

a. 22
b. 69
c. 23
d. 36

Explanation:

Step1: Use the property of parallel lines

Since \(CD\parallel EF\), \(\angle1+\angle2 = 180^{\circ}\) (consecutive interior angles are supplementary).

Step2: Substitute the given values

Substitute \(\angle1=4y - 12\) and \(\angle2 = 48^{\circ}\) into the equation:
\(4y-12 + 48=180\)
Simplify the left - hand side: \(4y+36 = 180\)

Step3: Solve for \(y\)

Subtract 36 from both sides: \(4y=180 - 36\), so \(4y=144\)
Divide both sides by 4: \(y=\frac{144}{4}=36\)

Answer:

D. 36