m∠1=48.5∘ and m∠2=75.25∘.
Since EC⎯⎯⎯⎯⎯ is an altitude, we know that ∠AEC=90∘ and ∠B+∠C=90∘.
We can rewrite the second equation in the problem as ∠C=3x+13.
Since ∠B+∠C=90∘, we can substitute to find:
∠B+3x+13=90∘
∠B=−3x+77∘
We can now use the first equation in the problem to solve for ∠1:
∠1=2x+7
We know that the sum of the angles in a triangle is 180∘, so we can plug in our two equations to find ∠2:
∠1+∠B+∠C=180∘
2x+7−3x+77+3x+13=180∘
4x+97=180∘
4x=83∘
x=20.75∘
Substitute to find ∠1:
∠1=2x+7
∠1=2(20.75∘)+7
∠1=41.5+7
∠1=48.5∘
Substitute to find ∠2:
∠2=3x+13
∠2=3(20.75∘)+13
∠2=62.25∘+13
∠2=75.25∘
Therefore, m∠1=48.5∘ and m∠2=75.25∘.