Question

The figure below shows
−−→
B
T
with point B at the intersection of
←−→
S
W
and
←→
R
U
.

The lines R-U and S-W intersect at B, angle B-T-U is 35 degrees and angle U-B-W is 50 degrees.

What is the measure of
∠
S
B
T
?

A.
85
°

B.
90
°

C.
110
°

D.
95
°

Answer 1

To find the measure of angle \( \angle SBT \), we can use the angles that are given:

1. \( \angle BTU = 35^\circ \)
2. \( \angle UBW = 50^\circ \)

We know that the sum of angles around point B (the intersection of lines RU and SW) must equal \( 360^\circ \).

At point B, the angles can be represented as follows:

- \( \angle BTU = 35^\circ \)
- \( \angle UBW = 50^\circ \)
- \( \angle SBW \) (which we want to find, as it equals \( \angle SBT \))
- The remaining angle at point B, which is \( \angle SBU = \angle BTU + \angle UBW \)

First, let's calculate \( \angle SBU \):

\[
\angle SBU = \angle BTU + \angle UBW = 35^\circ + 50^\circ = 85^\circ
\]

Now that we know \( \angle SBU = 85^\circ \), we can find \( \angle SBW \):

\[
\angle SBW = 180^\circ - \angle SBU
\]

Thus,

\[
\angle SBW = 180^\circ - 85^\circ = 95^\circ
\]

Now, since angle \( \angle SBT \) is equal to \( \angle SBW \), we conclude:

\[
\angle SBT = 95^\circ
\]

Therefore, the answer is:

**D. 95°**