Question

1. find the measure of each missing angle. m∠1 = __ m∠2 = m∠3 = m∠4 = m∠5 = __ 144° 56°

Explanation:

Step1: Use linear - pair property for ∠3

A linear - pair of angles sums to 180°. Since the angle adjacent to ∠3 is 144°, then $m\angle3=180 - 144=36^{\circ}$.

Step2: Use angle - sum property for the small triangle

The sum of interior angles of a triangle is 180°. In the small triangle with angles ∠3, 56°, and ∠4, we have $m\angle4=180-(36 + 56)=88^{\circ}$.

Step3: Use vertical - angle property for ∠2 and ∠4

Vertical angles are equal. So $m\angle2=m\angle4 = 88^{\circ}$.

Step4: Use angle - sum property for the large triangle

In the large triangle with angles ∠1, ∠2, and the angle adjacent to 56° (which is 124°), we know that the sum of interior angles of a triangle is 180°. So $m\angle1=180-(88 + 36)=56^{\circ}$.

Step5: Use linear - pair property for ∠5

The angle adjacent to 56° is 124°. Since ∠5 and the 124° angle are linear - pair, $m\angle5=180 - 124 = 56^{\circ}$.

Answer:

$m\angle1 = 56^{\circ}$
$m\angle2 = 88^{\circ}$
$m\angle3 = 36^{\circ}$
$m\angle4 = 88^{\circ}$
$m\angle5 = 56^{\circ}$