Question

1. rstu is a kite, m∠r = 160, and m∠s = 90. find m∠t.

Explanation:

Step1: Recall sum of interior angles

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

Step2: Set up angle - sum equation

Let $m\angle R = 160^{\circ}$, $m\angle S=90^{\circ}$, and $m\angle T = x$, $m\angle U$. In a kite, the non - vertex angles are equal. Let's assume $\angle R$ and $\angle T$ are vertex angles. Then the sum of the interior angles of the kite $RSTU$ is $m\angle R+m\angle S + m\angle T+m\angle U=360^{\circ}$. Since $\angle S=\angle U = 90^{\circ}$ (properties of a kite), we have $160 + 90+x + 90=360$.

Step3: Solve the equation

Combine like terms: $340 + x=360$. Subtract 340 from both sides: $x=360 - 340=20$.

Answer:

20