Question

Two angles are a linear pair. The measure of one angle is 10 more than 25% of the other. Find the measures of both angles.

Answer 1

Two angles forming a linear pair have measurements that add up to 180 degrees. One angle is 10 degrees more than 25% of the other. Solving this, the angles measure 136 degrees and 44 degrees respectively.

Step-by-step explanation:

When two angles form a linear pair, they are adjacent and their non-common sides form a straight line. This means that their measures add up to 180 degrees. If one angle's measure is 10 degrees more than 25% of the other angle, we can set up an equation to find their measures.

Let the measure of the first angle be x degrees. Therefore, the measure of the second angle would be 0.25x + 10 degrees. Since they form a linear pair, we can write:

x + 0.25x + 10 = 180

Combining like terms, we get:

1.25x + 10 = 180

Subtracting 10 from both sides, we find:

1.25x = 170

Dividing both sides by 1.25, we get:

x = 136

Therefore, the measure of the first angle is 136 degrees, and the measure of the second angle is:

0.25(136) + 10 = 34 + 10 = 44 degrees

The two angle measurements of the linear pair are 136 degrees and 44 degrees.

Answer 2

Linear pairs add up to 180°

1st angle = x

2nd angle = x+24 (24° more than the first)

The equation would be

1st angle + second angle = 180 Subbing in the expressions we came up with:

x+x+24 = 180