Question

1. two angles, ∠a and ∠b, are a linear pair. the measure of ∠a is 32°. write and solve an equation to determine the measure of ∠b. check your solution.

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to $180^\circ$. So, $m\angle A + m\angle B = 180^\circ$.

Step2: Substitute $m\angle A = 32^\circ$

Substitute into the equation: $32^\circ + m\angle B = 180^\circ$.

Step3: Solve for $m\angle B$

Subtract $32^\circ$ from both sides: $m\angle B = 180^\circ - 32^\circ = 148^\circ$.

Step4: Check the solution

Add $m\angle A$ and $m\angle B$: $32^\circ + 148^\circ = 180^\circ$, which satisfies the linear pair property.

Answer:

$\angle B = 148^\circ$