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In the figure below, line m is perpendicular to line n and both lines intersect line q at the same point. The measure of ∠1 is (3x - 10)°, and the measure of  ∠2 is (2x + 10)°. What is the measure of ∠3 ?

Question

In the figure below, line m is perpendicular to line n and both lines intersect line q at the same point. The measure of ∠1 is (3x - 10)°, and the measure of  ∠2 is (2x + 10)°. What is the measure of ∠3 ?

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Solution

The problem doesn't provide a figure, but based on the description, we can infer that ∠1 and ∠2 are adjacent angles on line q, which means they are supplementary. Therefore, their measures add up to 180°.

So, we can set up the equation (3x - 10) + (2x + 10) = 180.

Solving this equation:

5x = 180 x = 36

Now, since line m is perpendicular to line n, ∠3 is a right angle, which means it measures 90°.

This problem has been solved

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