Two angles, 1 and 2, in a diagram are supplementary. If m 1 = 77, what equation can you write to solve for m 2? Let m 2 = x
A. x + 77 = 90
B. x = 90 - 77
C. x + 77 = 180
D. x = 77
C. x + 77 = 180
The sum of the measures of angles A, B, and C should add up to 180.
Given that m A = 67, m B = (2x + 20), and m C = x, we can write the equation:
m A + m B + m C = 67 + (2x + 20) + x
Combining like terms:
3x + 87 = 180
Subtracting 87 from both sides:
3x = 93
Dividing both sides by 3:
x = 31
So the measure of angle B (m B) is 2x + 20 = 2(31) + 20 = 62 + 20 = 82.
Therefore, the correct answer is A. 82.
If there are two supplementary angles, D and E, where m D = (4x + 8) and m E = (x + 17), and F is a vertical angle with D, what is the measure of F?
A. 48
B. 124
C. 132
D. 31
There are angles whose measures add to 180. Their measures are: m A = 67, m B = (2x + 20), and m C = x. What is the measure of B?
A. 62
B. 82
C. 31
D. 180
If angles D and E are supplementary, their measures should add up to 180.
Given that m D = (4x + 8) and m E = (x + 17), we can write the equation:
m D + m E = (4x + 8) + (x + 17) = 5x + 25
Since angles D and F are vertical angles, they have equal measures. Therefore, angle F has the same measure as angle D, which is (4x + 8).
Setting up the equation:
4x + 8 = 5x + 25
To solve for x, subtract 4x from both sides:
8 = x + 25
Then, subtract 25 from both sides:
-17 = x
Now that we have the value of x, we can substitute it into the equation for angle F:
m F = 4x + 8 = 4(-17) + 8 = -68 + 8 = -60
Since we can't have negative angle measures, the measure of angle F is 360 - 60 = 300 degrees.
Therefore, the correct option is not provided.