Question

find the measure of ∠ptu.
(9x - 20)°
(2x + 36)°
a) what type of angle pair is shown?
alternate interior
alternate exterior
same side interior
same side exterior
corresponding
linear pair
vertical
b) are the angles congruent or supplementary?
congruent (∠1 = ∠2)
supplementary (∠1 + ∠2 = 180°)
c) solve for x.
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Explanation:

Step1: Identify angle - pair type

The angles $(9x - 20)^{\circ}$ and $(2x + 36)^{\circ}$ are alternate exterior angles.

Step2: Determine congruence/supplementary relationship

Alternate exterior angles are congruent when the lines are parallel. So, $9x-20 = 2x + 36$.

Step3: Solve for x

Subtract $2x$ from both sides: $9x-2x-20=2x - 2x+36$, which simplifies to $7x-20 = 36$. Then add 20 to both sides: $7x-20 + 20=36 + 20$, giving $7x=56$. Divide both sides by 7: $x=\frac{56}{7}=8$.

Step4: Find measure of $\angle PTU$

Substitute $x = 8$ into the expression for $\angle PTU=(9x - 20)^{\circ}$. So, $\angle PTU=9\times8-20=72 - 20=52^{\circ}$.

Answer:

a) Alternate Exterior
b) Congruent ($\angle1=\angle2$)
c) $x = 8$