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Math

QuestionFind the missing mD1 angles when mD3 is 98° and 165° given previous angle sets.

Studdy Solution

STEP 1

Assumptions1. The given sets of angles are pairs of corresponding angles. . Corresponding angles are equal when two lines are parallel and they are cut by a transversal.
3. The angles m1 and m3 are corresponding angles.

STEP 2

We first need to find the difference between the angles m1 and m for each given pair. This difference will be the same for all pairs of corresponding angles.Difference=m1−mDifference = m1 - m

STEP 3

Now, plug in the given values for the first pair of angles to calculate the difference.
Difference=118∘−20∘Difference =118^{\circ} -20^{\circ}

STEP 4

Calculate the difference for the first pair.
Difference=118∘−20∘=98∘Difference =118^{\circ} -20^{\circ} =98^{\circ}

STEP 5

We can check our assumption by calculating the difference for the other given pairs of angles. If the difference is the same for all pairs, our assumption is correct.
For the second pairDifference=15∘−65∘Difference =15^{\circ} -65^{\circ}Calculate the differenceDifference=15∘−65∘=−50∘Difference =15^{\circ} -65^{\circ} = -50^{\circ}This is not the same as the difference for the first pair, so our assumption was incorrect. The angles m1 and m3 are not corresponding angles.

STEP 6

Since the angles are not corresponding, we need to find another relationship between the angles. We can see that the sum of the angles m1 and m3 is the same for all given pairs.
Sum=m1+m3Sum = m1 + m3

STEP 7

Now, plug in the given values for the first pair of angles to calculate the sum.
Sum=118∘+20∘Sum =118^{\circ} +20^{\circ}

STEP 8

Calculate the sum for the first pair.
Sum=118∘+20∘=138∘Sum =118^{\circ} +20^{\circ} =138^{\circ}

STEP 9

We can check our assumption by calculating the sum for the other given pairs of angles. If the sum is the same for all pairs, our assumption is correct.
For the second pairSum=15∘+65∘Sum =15^{\circ} +65^{\circ}Calculate the sumSum=15∘+65∘=80∘Sum =15^{\circ} +65^{\circ} =80^{\circ}This is not the same as the sum for the first pair, so our assumption was incorrect. The angles m and m3 do not have a consistent sum.

STEP 10

Since neither the difference nor the sum of the angles is consistent, there must be a mistake in the problem. We cannot determine the missing angles without a consistent relationship between the angles m and m3.

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