Question

find the measures of the numbered angles in the kite. the figure is not drawn to scale. m∠1 = 102° (type an integer or a decimal.) m∠2 = □° (type an integer or a decimal.)

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Set up an equation

Let the measure of $\angle1 = 102^{\circ}$, one angle is $66^{\circ}$, and another is $90^{\circ}$. Let $m\angle2=x$. Then $66 + 90+102 + x=360$.

Step3: Simplify the left - hand side of the equation

$66+90 + 102+x=(66 + 90+102)+x=258+x$.

Step4: Solve for $x$

We have the equation $258+x = 360$. Subtract 258 from both sides: $x=360 - 258$. So $x = 102$.

Answer:

$m\angle2 = 102$