Question

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
Answer
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
Answer
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
Answered by GPT 3.5
C. x + 77 = 180
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.