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 kite - angle properties

In a kite, one pair of opposite angles are equal and the sum of the interior angles of a quadrilateral is 360°.

Step2: Set up an equation

Let the measure of ∠1 be \(x\), ∠2 be \(y\), and we know two other angles are 66° and 90°. So, \(x + y+66 + 90=360\). We are given \(x = 102\).

Step3: Solve for \(y\)

Substitute \(x = 102\) into the equation \(102+y + 66+90 = 360\). First, simplify the left - hand side: \(102+66 + 90+y=258 + y\). Then, solve the equation \(258 + y=360\) for \(y\). Subtract 258 from both sides: \(y=360 - 258\).
\(y = 102\)

Answer:

102