The figure below shows

Question

−−→
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 information given about the angles around point \( B \).

1. We know that angle \( \angle BTU = 35^\circ \).
2. We also know that angle \( \angle UBW = 50^\circ \).

Since angles around point \( B \) sum up to \( 360^\circ \), we can express it as: \[ \angle SBT + \angle BTU + \angle UBW + \angle WBS = 360^\circ \]

For our purposes, we only need the angles \( BTU \) and \( UBW \) to find \( \angle SBT \). The angles \( \angle BTU \) and \( \angle UBW \) are adjacent to \( \angle SBT \) on one side:

\[ \angle SBT + \angle BTU + \angle UBW = 180^\circ \]

Substituting the known values: \[ \angle SBT + 35^\circ + 50^\circ = 180^\circ \]

Combining the known angles: \[ \angle SBT + 85^\circ = 180^\circ \]

Now, isolate \( \angle SBT \): \[ \angle SBT = 180^\circ - 85^\circ = 95^\circ \]

So, the measure of \( \angle SBT \) is \( \boxed{95^\circ} \).