If angles 1 and 2 together form a right angle, then we know that:
m∠1 + m∠2 = 90°
Since we are given that m∠4 = 31°, we also know that angles 3 and 4 form a linear pair with angle 2 (angles on a straight line). Therefore:
m∠2 + m∠4 = 180°
Substituting the known value of m∠4 into this equation:
m∠2 + 31° = 180°
Now, solving for m∠2:
m∠2 = 180° - 31° m∠2 = 149°
Now, since angles 1 and 2 must add up to 90 degrees, we can use this fact to find m∠2:
However, here is a more straightforward approach to find the value of m∠2.
Since m∠4 is 31° and angles 2 and 5 must follow the sum of 180 degrees, we know that:
m∠2 + m∠4 = 180°
Since we already calculated m∠4:
m∠2 + 31° = 180° m∠2 = 180° - 31° m∠2 = 149°
However, since m∠1 + m∠2 = 90°, we need to notice that m∠2 must be calculated within angles 1 and 2 forming only part as right angles.
Let's recalculate to verify we need the other relation:
We know m∠1 + m∠2 = 90° and since m∠5 would simply be m∠2 either goes against or in pair with:
Thus, it should then lead to:
m∠2 is therefore 59° if we follow logical reasoning.
The final answer for m∠2 is:
59°
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