Question

A right angle intersects a line at point M.

A right angle intersects a vertical line at point M and forms 3 angles. From top to bottom going clockwise, the angles are 1, 90 degrees, 2.
Which statement is true about angles 1 and 2?

They are congruent.
They are right angles.
They are complementary.
They are supplementary.

Answer 1

I've attached an image showing the intersection and the angle.

Answer:

C: They are complementary

Explanation:

We can see from the image that angle 1, angle 2 and 90° are on a straight line. We know that sum of angles on a straight line is 180°. Thus;

∠1 + ∠2 + 90° = 180°

Rearranging, we have;

∠1 + ∠2 = 180° - 90°

Thus;

∠1 + ∠2 = 90°

Now, from angle proofs in trigonometry, it states that If the non-common sides of two adjacent angles add up to 90°, then it means that the angles are complementary.

In our problem here, sum of ∠1 and ∠2 equals 90°. Also, they are the non-common sides of 2 adjacent angles. Thus, we can say that they are complementary.

Explanation: