Question

1. quadrilateral park is an isosceles trapezoid. determine the measure of angle a, k and r. remember, all angles in a quadrilateral add up to 360°. angle a = angle k = angle r =

Explanation:

Step1: Recall isosceles trapezoid property

In an isosceles trapezoid, base - angles are equal. Let's assume $\angle P = 100^{\circ}$. Then the other non - base angle pair are equal.

Step2: Set up angle - sum equation

The sum of the interior angles of a quadrilateral is $360^{\circ}$. Let the measure of $\angle A=\angle P = 100^{\circ}$. Let the measure of $\angle K=\angle R=x$. Then $100 + 100+x + x=360$.

Step3: Simplify the equation

Combining like terms, we get $200 + 2x=360$. Subtract 200 from both sides: $2x=360 - 200=160$.

Step4: Solve for $x$

Divide both sides of the equation $2x = 160$ by 2. So $x = 80^{\circ}$.

Answer:

Angle A = $100^{\circ}$
Angle K = $80^{\circ}$
Angle R = $80^{\circ}$