Since two angles are complementary, the sum of their measures is 90 degrees. Thus, the equation to solve for the measure of ∠6 is:
m∠5 + m∠6 = 90
There are two complementary angles, ∠5 and ∠6. If m∠5 = 39 degrees, what equation can you write to solve for m∠6?
5 answers
Two angles, ∠1 and ∠2, in a diagram are supplementary. If m∠1 = 77 degrees, what equation can you write to solve for m∠2? Let m∠2 be x degrees
Since two angles are supplementary, the sum of their measures is 180 degrees. Thus, the equation to solve for the measure of ∠2 (x degrees) is:
m∠1 + m∠2 = 180
Substituting m∠1 with 77 degrees and m∠2 with x degrees, the equation becomes:
77 + x = 180
m∠1 + m∠2 = 180
Substituting m∠1 with 77 degrees and m∠2 with x degrees, the equation becomes:
77 + x = 180
5ere are angles whose measure add up to 180 degrees. their measures are m∠A = 67 degrees, m∠b = (2x + 20) degrees, and m∠C = x degrees. What is the measure of ∠B?
We know that the sum of the measures of angles A, B, and C is 180 degrees. Therefore, we can write the equation:
m∠A + m∠B + m∠C = 180
Substituting the given measures, we have:
67 + (2x + 20) + x = 180
Simplifying the equation:
67 + 2x + 20 + x = 180
Combining like terms:
3x + 87 = 180
Subtracting 87 from both sides of the equation:
3x = 93
Dividing both sides of the equation by 3:
x = 31
Now that we know the value of x, we can find the measure of ∠B:
m∠B = 2x + 20
Substituting x = 31:
m∠B = 2(31) + 20
m∠B = 62 + 20
m∠B = 82
Therefore, the measure of ∠B is 82 degrees.
m∠A + m∠B + m∠C = 180
Substituting the given measures, we have:
67 + (2x + 20) + x = 180
Simplifying the equation:
67 + 2x + 20 + x = 180
Combining like terms:
3x + 87 = 180
Subtracting 87 from both sides of the equation:
3x = 93
Dividing both sides of the equation by 3:
x = 31
Now that we know the value of x, we can find the measure of ∠B:
m∠B = 2x + 20
Substituting x = 31:
m∠B = 2(31) + 20
m∠B = 62 + 20
m∠B = 82
Therefore, the measure of ∠B is 82 degrees.