Question

What is the m∠QPT? Show work.

Answer 1

m∠QPT = 32°

Explanation:

∠QPT and ∠SPR are vertical angles, meaning that the measure of their angles are congruent (the same).

Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).

Step 1: Set the measure of the angles to equal each other.

`\implies m \angle QPT = m \angle SPR`

`\implies (2x+12) = (4x - 8)`

Step 2: Subtract 4x from both sides.

`\implies 2x-4x+12 = 4x - 4x - 8`

`\implies -2x+12 = - 8`

Step 3: Subtract 12 from both sides.

`\implies -2x+12-12 = - 8-12`

`\implies -2x = -20`

Step 4: Divide both sides by -2.

`\implies (-2x)/(-2) = (-20)/(-2)`

`\implies x = 10`

Step 5: Find the measure of ∠QPT by substituting 10 for x.

`\implies [2(10)+12]^(\circ)`

`\implies 32^(\circ)`

Therefore, the measure of ∠QPT is 32°.