Question

the figure shows two intersecting lines. write an equation to show how ( mangle1 ) and ( mangle2 ) are related. ( mangle1 + mangle2 = 180^{circ} ) when the measures of two angles sum to ( 180^{circ} ) they are supplementary. ( angle1 ) and ( angle2 ) are supplementary angles. ( mangle1 = 137^{circ} ). find ( mangle2 ). ( mangle2 = )

Explanation:

Step1: Use the supplementary - angle relationship

We know that \(m\angle1 + m\angle2=180^{\circ}\) (from the property of supplementary angles).

Step2: Substitute the value of \(m\angle1\)

Given \(m\angle1 = 137^{\circ}\), substitute it into the equation \(m\angle1 + m\angle2=180^{\circ}\). So, \(137^{\circ}+m\angle2 = 180^{\circ}\).

Step3: Solve for \(m\angle2\)

Subtract \(137^{\circ}\) from both sides of the equation. \(m\angle2=180^{\circ}-137^{\circ}\).

$$m\angle2 = 43^{\circ}$$

Answer:

\(43\)