Question

Solve equations with adjacent angles practice

Answer 1

Sure! Here are a couple of examples of solving equations with adjacent angles:

Example 1:
Given that the measure of one angle is 40 degrees more than the measure of its adjacent angle, find the measures of the angles.

Let x be the measure of the smaller angle.
Then, the measure of the larger angle is x + 40 degrees.

Since the two angles are adjacent, their measures add up to 180 degrees:

x + (x + 40) = 180
2x + 40 = 180
2x = 180 - 40
2x = 140
x = 70

Therefore, the smaller angle measures 70 degrees, and the larger angle measures 70 + 40 = 110 degrees.

Example 2:
Given that the measure of an angle is three times the measure of its adjacent angle minus 10 degrees, find the measures of the angles.

Let x be the measure of the smaller angle.
Then, the measure of the larger angle is 3x - 10 degrees.

Since the two angles are adjacent, their measures add up to 180 degrees:

x + (3x - 10) = 180
4x - 10 = 180
4x = 180 + 10
4x = 190
x = 190/4
x = 47.5

Therefore, the smaller angle measures 47.5 degrees, and the larger angle measures 3(47.5) - 10 = 132.5 degrees.

I hope this helps! Let me know if you have any other questions.