Question

kite and trapezoid properties

1. trap is a trapezoid.

equation to find x:

x= ______,
equation to find y:

Explanation:

Step1: Identify trapezoid angle property

In a trapezoid, consecutive angles between the bases are supplementary (sum to $180^\circ$). For sides $RA \parallel TP$, $\angle R + \angle T = 180^\circ$ and $\angle A + \angle P = 180^\circ$.

Step2: Set up equation for y

Use $\angle A + \angle P = 180^\circ$:
$$(8y-12) + (5y-2) = 180$$

Step3: Solve for y

Combine like terms and isolate y:
$$13y - 14 = 180$$
$$13y = 194$$
$$y = \frac{194}{13} \approx 14.92$$

Step4: Set up equation for x

Use $\angle R + \angle T = 180^\circ$:
$$130 + x = 180$$

Step5: Solve for x

Isolate x:
$$x = 180 - 130$$
$$x = 50$$

Answer:

Equation to find x: $\boldsymbol{130 + x = 180}$
$\boldsymbol{x=50}$
Equation to find y: $\boldsymbol{(8y-12) + (5y-2) = 180}$
$\boldsymbol{y=\frac{194}{13}}$ (or approximately $\boldsymbol{14.92}$)