Question

find the measures of angle 3 and angle 4. the measure of angle 3 is . (simplify your answer. type an integer or a decimal.) (the figure is not to scale.)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the given triangle, if we assume the three interior angles are the ones with measures 47°, 51° and the angle adjacent to angle 4. Let the angle adjacent to angle 4 be \(x\). Then \(x + 47^{\circ}+51^{\circ}=180^{\circ}\).

Step2: Calculate the value of \(x\)

\[

$$\begin{align*} x&=180-(47 + 51)\\ x&=180 - 98\\ x&=82^{\circ} \end{align*}$$

\]

Step3: Use the linear - pair property

Angle 4 and \(x\) form a linear - pair (a straight - line angle which is 180°). So, if \(x = 82^{\circ}\), then angle 4 \(=180 - 82=98^{\circ}\).

Step4: Use the linear - pair property for angle 3

Angle 3 and the 51° angle form a linear - pair. So, angle 3 \(=180 - 51=129^{\circ}\)

Answer:

The measure of angle 3 is 129° and the measure of angle 4 is 98°