Question

one angle of a linear pair is 10 more than two thirds the other angle. find the measure if both angles

Answer 1

One Angle = 110°

Other Angle = 70°

Explanation:

A linear pair means that two angles are in a straight line (or, a straight angle).

A straight line is 180 degrees.

THey are supplementary.

We can say one angle is "a" and another one is "b".

One angle is 10 MORE THAN 2/3rds of the other, we can write:

`a=(2)/(3)b+10`

Also, since they are supplementary (add up to 180), we can write:

a + b = 180

We can now substitute 1st equation in this one and find b:

`a+b=180\\((2)/(3)b+10)+b=180\\(2)/(3)b+b=180-10\\(5)/(3)b=170\\b=(170)/((5)/(3))\\b=170*(3)/(5)\\b=110`

Since a + b = 180, we can write:

a + 110 = 180

so,

a = 180 - 110

a = 70

Thus,

One Angle = 110°

Other Angle = 70°