Question

1. find the measure of y.

120°
85°
53°
85°
122°
102°
138°

Explanation:

Step1: Recall polygon - angle sum formula

The sum of interior angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Set up an equation

Let the four - angles of the quadrilateral be $120^{\circ}$, $85^{\circ}$, $53^{\circ}$, and $y^{\circ}$. Then $120 + 85+53 + y=360$.

Step3: Simplify the left - hand side

$120+85 + 53=258$. So the equation becomes $258 + y=360$.

Step4: Solve for y

Subtract 258 from both sides: $y=360 - 258=102^{\circ}$.

Answer:

$102^{\circ}$