Answer: To find the measures of the two angles described in the problem, we can set up an equation based on the relationship between a angle and its supplementary angle:
Let's denote:
- The measure of the angle as A
- The measure of its supplementary angle as B
According to the problem:
- The angle A measures 46° less than its supplementary angle B.
- The sum of an angle and its supplementary angle is 180°.
Setting up the equation:
A = B - 46 (since A measures 46° less than B)
A + B = 180 (since the sum of A and B is 180°)
Now, we can substitute the value of A from the first equation into the second equation:
(B - 46) + B = 180
2B - 46 = 180
2B = 226
B = 113
Now, we can find the measure of angle A by substituting B back into the first equation:
A = 113 - 46
A = 67
Therefore, the measure of the angle A is 67° and the measure of its supplementary angle B is 113°.
Step-by-step explanation:
