Math 7B Unit 3 Study Guide

Question

4. Two adjacent angles, 41 and < 2, form a resulting angle with measure 161°. If mL1 = (4)° and mz2 = (4n + 1)°, what are the two unknown angle measures?
(m<1 means the measurement of angle 1)
m21
J*. m/2

Answer 1

To find the unknown angle measures, we can use the fact that adjacent angles add up to 180 degrees.

The given angles are 41° and < 2 (which means angle 2).

We are given that the resulting angle is 161°, so we can set up an equation:
m1 + m2 = 161°

Substituting the given angle measures, we have:
41° + m2 = 161°

To solve for m2, we can subtract 41 from both sides:
m2 = 120°

So, the measure of angle 2 is 120°.

To find m/2 (the measure of half of angle 2), we can divide the measure of angle 2 by 2:
m/2 = 120° / 2 = 60°

Therefore, the unknown angle measures are:
m21 = 120°
m/2 = 60°