Questions: Find the measure of each numbered angle. m<1= m∠2= m∠3=

Transcript text: Find the measure of each numbered angle. \[ m<1= \] $m \angle 2=$ \[ m \angle 3= \]

Solution

Step 1: Find the measure of angle 1.

The sum of the angles in triangle MQP is 180°. Therefore, the measure of angle 1 is: $m\angle 1 = 180^\circ - 66^\circ - 58^\circ = 56^\circ$.

Step 2: Find the measure of angle 2.

Angles 1 and 2 are vertical angles, therefore they are congruent. $m\angle 2 = m\angle 1 = 56^\circ$.

Step 3: Find the measure of angle 3.

The sum of the angles in triangle NQO is 180°. Therefore, the measure of angle 3 is: $m\angle 3 = 180^\circ - 50^\circ - 56^\circ = 74^\circ$.

$m\angle 1 = 56^\circ$, $m\angle 2 = 56^\circ$, $m\angle 3 = 74^\circ$

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