Question

1. find the measure of each missing angle. m∠1 =

m∠2 =
m∠3 =
m∠4 =
m∠5 =

Explanation:

Step1: Find \(m\angle5\)

Use the linear - pair relationship. \(\angle5 + 144^{\circ}=180^{\circ}\). So, \(m\angle5=180^{\circ}- 144^{\circ}=36^{\circ}\).

Step2: Find \(m\angle4\)

Since the triangle with \(\angle4\), \(\angle5\), and \(56^{\circ}\) is a triangle, and the sum of angles in a triangle is \(180^{\circ}\). Then \(m\angle4=180^{\circ}-(m\angle5 + 56^{\circ})\). Substitute \(m\angle5 = 36^{\circ}\), we get \(m\angle4=180^{\circ}-(36^{\circ}+56^{\circ})=88^{\circ}\).

Step3: Find \(m\angle3\)

Because of the side - length equality (marked by tick - marks), \(\angle3=\angle4\) (isosceles triangle property). So \(m\angle3 = 88^{\circ}\).

Step4: Find \(m\angle1\)

Since the large triangle has two equal sides (marked by tick - marks), \(\angle1=\angle2\). Also, for the large triangle, \(\angle1+\angle2+(180^{\circ}-m\angle3)=180^{\circ}\). Substitute \(m\angle3 = 88^{\circ}\), then \(\angle1+\angle2 + 92^{\circ}=180^{\circ}\), and \(\angle1+\angle2=88^{\circ}\). Since \(\angle1=\angle2\), \(m\angle1=\frac{88^{\circ}}{2}=44^{\circ}\).

Step5: Find \(m\angle2\)

Since \(\angle1=\angle2\) (isosceles triangle property), \(m\angle2 = 44^{\circ}\).

Answer:

\(m\angle1 = 44^{\circ}\), \(m\angle2 = 44^{\circ}\), \(m\angle3 = 88^{\circ}\), \(m\angle4 = 88^{\circ}\), \(m\angle5 = 36^{\circ}\)