Question

"Angles < 3 and < 4 form a linear pair. The measure of < 3 is four more than three times the measure of < 4. Find the measure of each angle? Let M1 = x represent the measure of < 3, and let M2 = y represent the measure of < 4."

Answer 1

To find the measures of angles < 3 and < 4, we can set up an equation based on the given information and solve. Angle < 3 is four more than three times angle < 4. By substituting the values back into the equation, we can find that the measure of angle < 3 is 136 degrees and the measure of angle < 4 is 44 degrees.

Step-by-step explanation:

To solve this problem, we need to set up an equation based on the given information. We know that angles < 3 and < 4 form a linear pair, which means they are adjacent angles that add up to 180 degrees. Let's set up the equation:

M1 + M2 = 180 (Equation 1)

We are also given that the measure of angle < 3 (represented by M1) is four more than three times the measure of angle < 4 (represented by M2). We can write this as:

M1 = 3M2 + 4 (Equation 2)

Now, we can substitute equation 2 into equation 1 to solve for the measures of the angles:

3M2 + 4 + M2 = 180

4M2 + 4 = 180

4M2 = 176

M2 = 44

Substituting the value of M2 back into equation 2, we can find M1:

M1 = 3(44) + 4

M1 = 136

Therefore, the measure of angle < 3 (M1) is 136 degrees, and the measure of angle < 4 (M2) is 44 degrees.