Question

Two angles form a linear pair. One of them is 4 more than 3 times the other. What is the measure of the smaller angle?

Answer 1

The measure of the smaller angle in a linear pair, where one angle is 4 more than 3 times the other, is 44 degrees.

Step-by-step explanation:

To solve the problem, let's denote the measure of the smaller angle as x degrees. Since the angles form a linear pair, they add up to 180 degrees. The larger angle is 4 more than 3 times the smaller angle, so we can express it as 3x + 4 degrees.

According to the linear pair postulate, the sum of the two angles is 180 degrees, which gives us the equation:

x + (3x + 4) = 180

Combining like terms, we get:

4x + 4 = 180

Subtracting 4 from both sides, we obtain:

4x = 176

Dividing both sides by 4 to solve for x gives us:

x = 44

Therefore, the measure of the smaller angle is 44 degrees.

Answer 2

Answer: The measure of the smaller angle is 44°.

Step-by-step explanation:

If two angles, A and B, form a linear pair, this means that:

A + B = 180°.

Now, let's suppose that A is the larger one, so A > B.

"One of them is 4 more than 3 times the other"

A = 4 + 3*B

Then we have a system of equations:

A + B = 180

A = 4 + 3*B

First we could replace the second equation into the first one.

A + B = 180

(4 + 3*B) + B = 180

4 + 4*B = 180

4*B = 180 - 4 = 176

B = 176/4 = 44

Then we have that the angles are:

A = 136° and B = 44°

The measure of the smaller angle is 44°.