Question

1. what is the value of a if ∠4 = 3a + 40 and ∠5 = 2a + 50 are consecutive interior angles?

a. 22
b. 14
c. 18
d. 10

Explanation:

Step1: Recall consecutive - interior angles property

Consecutive interior angles are supplementary, so \(\angle4+\angle5 = 180^{\circ}\).

Step2: Substitute angle expressions

Substitute \(\angle4=3a + 40\) and \(\angle5=2a + 50\) into the equation: \((3a + 40)+(2a+50)=180\).

Step3: Simplify the left - hand side

Combine like terms: \(3a+2a + 40 + 50=180\), which gives \(5a+90 = 180\).

Step4: Solve for \(a\)

Subtract 90 from both sides: \(5a=180 - 90\), so \(5a=90\). Then divide both sides by 5: \(a=\frac{90}{5}=18\).

Answer:

c. 18