Question

what is the measure of ∠2 in degrees? the measure of ∠1 is (10x + 8)° and the measure of ∠3 is (12x - 10)°

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So \(10x + 8=12x-10\).

Step2: Solve for \(x\)

Subtract \(10x\) from both sides: \(8 = 2x-10\).
Add \(10\) to both sides: \(18=2x\).
Divide by \(2\): \(x = 9\).

Step3: Find \(\angle1\)

Substitute \(x = 9\) into \(10x + 8\): \(10\times9+8=98^{\circ}\).

Step4: Use linear - pair property

\(\angle1+\angle2 = 180^{\circ}\) (linear pair).
So \(\angle2=180-(10x + 8)\).
Substitute \(x = 9\): \(\angle2=180 - 98=82^{\circ}\).

Answer:

\(82\)