Math

QuestionIf 1\angle 1 is 123123^{\circ} and is a supplement of 2\angle 2, find m3m \angle 3 where 2\angle 2 is a complement of 3\angle 3.

Studdy Solution

STEP 1

Assumptions1. 1\angle1 is a supplement of \angle . m1=123m \angle1 =123^{\circ}
3. \angle is a complement of 3\angle3

STEP 2

The definition of supplementary angles is that the sum of their measures is 180180^{\circ}. So, we can write the equation for the measure of 2\angle2 as followsm2=180m1m \angle2 =180^{\circ} - m \angle1

STEP 3

Now, plug in the given value for m1m \angle1 to calculate m2m \angle2.
m2=180123m \angle2 =180^{\circ} -123^{\circ}

STEP 4

Calculate the measure of 2\angle2.
m2=180123=57m \angle2 =180^{\circ} -123^{\circ} =57^{\circ}

STEP 5

The definition of complementary angles is that the sum of their measures is 9090^{\circ}. So, we can write the equation for the measure of 3\angle3 as followsm3=90m2m \angle3 =90^{\circ} - m \angle2

STEP 6

Now, plug in the calculated value for m2m \angle2 to calculate m3m \angle3.
m3=9057m \angle3 =90^{\circ} -57^{\circ}

STEP 7

Calculate the measure of 3\angle3.
m3=9057=33m \angle3 =90^{\circ} -57^{\circ} =33^{\circ}So, the measure of 3\angle3 is 3333^{\circ}.

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