Question

8 fill in the blank 1 point find all missing angles. 95° 38° m∠1 = type your answer m∠2 = 85 m∠3 = 95 m∠4 = 85 m∠5 = 36

Explanation:

Step1: Use the triangle angle - sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). For the triangle with angle \(144^{\circ}\) and a right - angle (\(90^{\circ}\)) and \(\angle5\), we know that \(144^{\circ}\) is an exterior angle. The adjacent interior angle to \(144^{\circ}\) is \(180 - 144=36^{\circ}\) (linear pair).

Step2: Find \(\angle1\)

For the triangle with \(\angle2 = 85^{\circ}\), \(\angle5=36^{\circ}\) and \(\angle1\). Using the triangle angle - sum formula \(m\angle1+85 + 36=180\).

$$m\angle1=180-(85 + 36)$$

$$m\angle1=180 - 121$$

$$m\angle1 = 59^{\circ}$$

Answer:

\(m\angle1 = 59\)