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Math Asked by a SnapAndSolve user · about 2 hours ago

Given that: ∠1 ≅ ∠2 ∠3 ≅ ∠4 ∠5 ≅ ∠6 m∠2 = 3x + 10 m∠4 = 2x + 30 Find the m∠2 in degrees.

Given that:
∠1 ≅ ∠2
∠3 ≅ ∠4
∠5 ≅ ∠6
m∠2 = 3x + 10
m∠4 = 2x + 30
Find the m∠2 in degrees.

Answer

To find the measure of ∠2, we use the given information that ∠1 ≅ ∠2 and ∠3 ≅ ∠4. Since ∠3 ≅ ∠4, we have:

m∠3 = m∠4 = 2x + 30

Since ∠1 ≅ ∠2, we have:

m∠1 = m∠2 = 3x + 10

Since the angles are congruent, set the expressions equal to each other:

3x + 10 = 2x + 30

Solve for x:

3x + 10 = 2x + 30
3x - 2x = 30 - 10
x = 20

Substitute x back into the expression for m∠2:

m∠2 = 3(20) + 10 = 60 + 10 = 70 degrees

Therefore, the measure of ∠2 is 70 degrees.

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