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QuestionAngle 1 and Angle 2 are supplementary with m∠2=104∘m \angle 2=104^{\circ}. Find m∠1m \angle 1. Also, find m∠ABDm \angle A B D for the linear pair.

Studdy Solution

STEP 1

Assumptions1. Angle1 and Angle are supplementary, meaning they add up to180 degrees. . The measure of Angle is given as104 degrees.
3. We are asked to find the measure of Angle1.

STEP 2

We can find the measure of Angle1 by subtracting the measure of Angle2 from180 degrees, since supplementary angles add up to180 degrees.
m∠1=180∘−m∠2m \angle1 =180^{\circ} - m \angle2

STEP 3

Now, plug in the given value for the measure of Angle2 to calculate the measure of Angle1.
m∠1=180∘−104∘m \angle1 =180^{\circ} -104^{\circ}

STEP 4

Calculate the measure of Angle1.
m∠1=180∘−104∘=76∘m \angle1 =180^{\circ} -104^{\circ} =76^{\circ}The measure of Angle1 is76 degrees.

STEP 5

Assumptions for the second part of the problem1. The angles form a linear pair, meaning they add up to180 degrees.
2. We are asked to find the measure of Angle ABD.

STEP 6

We can find the measure of Angle ABD by subtracting the measure of Angle BDC from180 degrees, since angles that form a linear pair add up to180 degrees.
m∠ABD=180∘−m∠BDCm \angle ABD =180^{\circ} - m \angle BDC

STEP 7

Now, plug in the given value for the measure of Angle BDC to calculate the measure of Angle ABD.
m∠ABD=180∘−m∠BDCm \angle ABD =180^{\circ} - m \angle BDC

STEP 8

Calculate the measure of Angle ABD.
m∠ABD=180∘−m∠BDCm \angle ABD =180^{\circ} - m \angle BDCThe measure of Angle ABD is the result of the above calculation.

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