Question

The interior angle of point B measures (3x-7) degrees and the interior angle of point D measures (x+15) degrees. What is the value of angle D?



(1 point)
Responses

26
26

11
11

22
22

43
43

Answer 1

To find the value of angle D, we first need to determine the value of \( x \) by using the information about the interior angles at points B and D.

From the problem, we have:
- Angle at point B: \( 3x - 7 \)
- Angle at point D: \( x + 15 \)

Assuming that points B and D are part of a polygon and the sum of the interior angles at these points equals 180 degrees (as a simple case), the equation would be:

\[
(3x - 7) + (x + 15) = 180
\]

Now we simplify and solve for \( x \):

1. Combine like terms:
\[
3x - 7 + x + 15 = 180
\]
\[
4x + 8 = 180
\]

2. Subtract 8 from both sides:
\[
4x = 172
\]

3. Divide by 4:
\[
x = 43
\]

Now that we have the value of \( x \), we can find the measure of angle D using the expression for angle D:

\[
D = x + 15 = 43 + 15 = 58
\]

However, since none of the provided options match 58. It's possible that the angles at points B and D should sum to a different value, or another condition needs to be applied.

For just angle D from the provided options and if we assess it using typical angle measures:

Attempting again with refreshing \( x \). If you mean that angles \( 3x - 7 \) and \( x + 15\) are simply equal for contrast or a smaller polygon's angle:

If they need to be equal:
\[
3x - 7 = x + 15
\]

1. Rearranging gives:
\[
3x - x = 15 + 7
\]
\[
2x = 22
\]
\[
x = 11
\]

Then now substituting for angle D:
\[
D = 11 + 15 = 26
\]

Checking the options, angle D is \( 26 \).

Thus, the correct answer is:
**26**.