Question

6 fill in the blank 1 point find the measure of each missing angle. 144° 56° m∠1 = type your answer... m∠2 = type your answer... m∠3 = type your answer... m∠4 = type your answer... m∠5 = type your answer...

Explanation:

Step1: Find \(m\angle5\)

Use the linear - pair relationship. If two angles form a linear pair, their sum is \(180^{\circ}\).
\(m\angle5 = 180^{\circ}-144^{\circ}\)
\(m\angle5=36^{\circ}\)

Step2: Find \(m\angle3\)

Use the linear - pair relationship. \(m\angle3 = 180^{\circ}-56^{\circ}\)
\(m\angle3 = 124^{\circ}\)

Step3: Find \(m\angle1\)

Since the sides adjacent to \(\angle1\) and the side adjacent to the angle of \(144^{\circ}\) (in the non - overlapping part) are equal (marked with the same tick), \(\angle1\) and the non - overlapping part of the \(144^{\circ}\) angle are equal.
\(m\angle1=36^{\circ}\)

Step4: Find \(m\angle4\)

Since the sides adjacent to \(\angle4\) and the side adjacent to \(56^{\circ}\) are equal (marked with the same tick), \(\angle4 = 56^{\circ}\)

Step5: Find \(m\angle2\)

Use the triangle - angle sum property. The sum of angles in a triangle is \(180^{\circ}\).
Let the triangle with angles \(\angle1,\angle2,\angle3\).
\(m\angle2=180^{\circ}-m\angle1 - m\angle3\)
Substitute \(m\angle1 = 36^{\circ}\) and \(m\angle3=124^{\circ}\)
\(m\angle2=180^{\circ}-36^{\circ}-124^{\circ}\)
\(m\angle2 = 20^{\circ}\)

Answer:

\(m\angle1 = 36^{\circ}\)
\(m\angle2=20^{\circ}\)
\(m\angle3 = 124^{\circ}\)
\(m\angle4 = 56^{\circ}\)
\(m\angle5=36^{\circ}\)