measure of Angle A is 24° more than twice Measure of angle B. Angle A and Angle B are supplementary. Find the measure of each angle.
(1 point)
Responses
measure of angle A equals 128 degrees; measure of angle B equals 52 degrees
Image with alt text: measure of angle A equals 128 degrees ; Image with alt text: measure of angle B equals 52 degrees
measure of angle A equals 120 degrees; measure of angle B equals 60 degrees
Image with alt text: measure of angle A equals 120 degrees ; Image with alt text: measure of angle B equals 60 degrees
measure of angle A equals 102 degrees; measure of angle B equals 78 degrees
Image with alt text: measure of angle A equals 102 degrees ; Image with alt text: measure of angle B equals 78 degrees
measure of angle A equals 114 degrees; measure of angle B equals 66 degrees
The correct answer is:
measure of angle A equals 102 degrees; measure of angle B equals 78 degrees
To solve this problem, we can set up an equation. Let's say the measure of angle B is x degrees. According to the information given, the measure of angle A is 24 degrees more than twice the measure of angle B. So, angle A can be represented as 2x + 24.
The problem also states that angle A and angle B are supplementary, which means they add up to 180 degrees. So, we can write the equation:
2x + 24 + x = 180
Combining like terms, we have:
3x + 24 = 180
Subtracting 24 from both sides, we get:
3x = 156
Dividing both sides by 3, we find:
x = 52
So, the measure of angle B is 52 degrees.
To find the measure of angle A, we can substitute this value of x back into the expression for angle A:
A = 2x + 24
A = 2(52) + 24
A = 104 + 24
A = 128
Therefore, the measure of angle A is 128 degrees and the measure of angle B is 52 degrees.