Question

I am very stuck on this

The measure of an angle is twenty-three times the measure of its supplementary angle. What is the measure of each angle?

Answer 1

So, supplementary angles is an angle pair that adds up to 180 degrees.

If one of the angles is 23 times larger than the other angle, then the other angle would be 1 times larger, due to the reflexive prop.

So combined, the angle pair is 24 times larger than the small angle. And since we know that the supplementary angle is 180, it's something that easy math can solve.

For the small angle:

180 / 24 --> 7.5 degrees.

Now with the big angle that 23 times that:

7.5 * 23 --> 172.5 degrees.

Answer 2

∡'s are 172.5° and 7.5°

Explanation:

x = 23(180-x)

x = 4140 - 23x

add 23x to each side

24x = 4140

x = 4140/24

x = 172.5