Question

for exercises 3 - 5, use the diagram to determine the measures of the given angles. 3. m∠eam 4. m∠mas 5. m∠tae

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. The angle opposite to the \(118^{\circ}\) angle is also \(118^{\circ}\). Adjacent angles on a straight - line are supplementary (sum to \(180^{\circ}\)).

Step2: Find \(m\angle EAM\)

\(\angle EAM\) and the \(118^{\circ}\) angle are adjacent angles on a straight - line. Let \(m\angle EAM=x\). Then \(x + 118^{\circ}=180^{\circ}\), so \(x=180^{\circ}-118^{\circ}=62^{\circ}\).

Step3: Find \(m\angle MAS\)

\(\angle MAS\) and \(\angle EAM\) are vertical angles. Since vertical angles are equal, \(m\angle MAS = m\angle EAM=62^{\circ}\).

Step4: Find \(m\angle TAE\)

\(\angle TAE\) and the \(118^{\circ}\) angle are vertical angles. So \(m\angle TAE = 118^{\circ}\).

Answer:

1. \(m\angle EAM = 62^{\circ}\)
2. \(m\angle MAS = 62^{\circ}\)
3. \(m\angle TAE = 118^{\circ}\)