Question

1. if ∠7 = 5y - 10 and ∠8 = 2y + 30 are consecutive interior angles, what is the value of y? round to the nearest whole number.

a. 50
b. 40
c. 23
d. 20

Explanation:

Step1: Recall angle - property

Consecutive interior angles are supplementary, so $\angle7+\angle8 = 180^{\circ}$.

Step2: Substitute angle - expressions

Substitute $\angle7 = 5y - 10$ and $\angle8=2y + 30$ into the equation: $(5y - 10)+(2y + 30)=180$.

Step3: Simplify the left - hand side

Combine like terms: $5y+2y-10 + 30=180$, which gives $7y+20 = 180$.

Step4: Solve for y

Subtract 20 from both sides: $7y=180 - 20=160$. Then divide both sides by 7: $y=\frac{160}{7}\approx22.86$.

Step5: Round to the nearest whole number

Rounding $\frac{160}{7}\approx23$.

Answer:

c. 23