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QuestionFind ∠AMH\angle AMH in isosceles triangles △MAT\triangle MAT and △MHT\triangle MHT with m∠MHT=88∘m \angle MHT=88^{\circ} and m∠MAT=64∘m \angle MAT=64^{\circ}.

Studdy Solution

STEP 1

Assumptions1. △MA\triangle M A and △MH\triangle M H are isosceles triangles. . m∠MH=88∘m \angle M H=88^{\circ} and m∠MA=64∘m \angle M A=64^{\circ}.
3. We are asked to find m∠AMHm \angle A M H.

STEP 2

In an isosceles triangle, the base angles are equal. Therefore, we can find the measure of ∠HM\angle H M and ∠MA\angle M A by subtracting the given angle from180 and dividing by2.
m∠HM=180∘−m∠MH2m \angle H M = \frac{180^{\circ} - m \angle M H}{2}m∠MA=180∘−m∠MA2m \angle M A = \frac{180^{\circ} - m \angle M A}{2}

STEP 3

Now, plug in the given values for m∠MHm \angle M H and m∠MAm \angle M A to calculate m∠HMm \angle H M and m∠MAm \angle M A.
m∠HM=180∘−88∘2m \angle H M = \frac{180^{\circ} -88^{\circ}}{2}m∠MA=180∘−64∘2m \angle M A = \frac{180^{\circ} -64^{\circ}}{2}

STEP 4

Calculate the values of m∠HMm \angle H M and m∠MAm \angle M A.
m∠HM=92∘2=46∘m \angle H M = \frac{92^{\circ}}{2} =46^{\circ}m∠MA=116∘2=58∘m \angle M A = \frac{116^{\circ}}{2} =58^{\circ}

STEP 5

Now, we can find the measure of ∠AMH\angle A M H by adding the measures of ∠HM\angle H M and ∠MA\angle M A.
m∠AMH=m∠HM+m∠MAm \angle A M H = m \angle H M + m \angle M A

STEP 6

Plug in the values for m∠HMm \angle H M and m∠MAm \angle M A to calculate m∠AMHm \angle A M H.
m∠AMH=46∘+58∘m \angle A M H =46^{\circ} +58^{\circ}

STEP 7

Calculate the measure of ∠AMH\angle A M H.
m∠AMH=46∘+58∘=104∘m \angle A M H =46^{\circ} +58^{\circ} =104^{\circ}So, the measure of ∠AMH\angle A M H is 104∘104^{\circ}.

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