Question

If m<4 = 15, find the measure of <2

Answer 1

75°

Explanation:

Angle properties can help us find the measure of an unknown angle.

Vertical Angles

Before we find the measurement of angle 2, we need to find angle 1. Angle 1 and angle 4 are vertical angles.

• Vertical angles are angles formed by 2 intersecting lines.

We know that 1 and 4 are vertical angles because they are formed by the same lines. Vertical angles are always congruent. This means that if angle 4 is 15°, then angle 1 must equal 15°.

Complementary Angles

Now that we know angle 1, we can find angle 2. Angles 1 and 2 are complementary angles.

• Complementary angles are angles that sum to 90°.

We can tell that 1 and 2 are complementary angles because together they form a right angle. Using this information, we can set up an equation.

• 15 + x = 90
• x = 75

This shows that angle 2 must equal 75°.