Question

1. find the missing measure. 2. find the missing measure. 3. find the missing measures.

Explanation:

Step1: Recall angle - sum property

The sum of angles in a right - angled triangle (where one angle is 90°) is 180°. In the first figure, we know one angle is 65° and the right - angle is 90°. Let the missing angle be \(x\). Then \(x + 65+90 = 180\).

Step2: Solve for \(x\) in the first figure

\[

$$\begin{align*} x&=180-(65 + 90)\\ x&=180 - 155\\ x&=25 \end{align*}$$

\]

Step3: Recall vertical - angle property

In the second figure, vertical angles are equal. If one angle is 51°, then the angle opposite to it (\(x\)) is also 51° because vertical angles are congruent.

Step4: Recall supplementary - angle property

In the third figure, the angle \(x\) and 107° are supplementary (a straight - line is 180°). So \(x+107 = 180\), then \(x=180 - 107=73\). Also, the angle \(y\) and \(x\) are vertical angles, so \(y = x = 73\).

Answer:

1. \(x = 25\)
2. \(x = 51\)
3. \(x = 73\), \(y = 73\)