Question

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given: ∠a = 4x + 5
∠b = x - 10
and ∠a and ∠b are consecutive interior angles
find: the measure of each angle

Explanation:

Step1: Recall consecutive interior angles property

Consecutive interior angles are supplementary, so $\angle A + \angle B = 180^\circ$.

Step2: Substitute angle expressions

$4x + 5 + x - 10 = 180$

Step3: Simplify and solve for x

$5x - 5 = 180 \implies 5x = 185 \implies x = 37$

Step4: Calculate $\angle A$

$\angle A = 4(37) + 5 = 153^\circ$

Step5: Calculate $\angle B$

$\angle B = 37 - 10 = 27^\circ$

Answer:

$\angle A = 153^\circ$, $\angle B = 27^\circ$