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audreywizzy
15.12.2021 •
Mathematics
In the figure MN | OP and ZOST-73
Find the measure of ZMTS and ZSTN
M
T
73°
S
R
N
ZMTS = 107° and ZSTN = 107°
ZMTS = 107° and ZSTN = 73°
ZMTS = 73° and ZSTN = 73°
O ZMTS = 73° and ZSTN = 107°
Solved
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Ответ:
B
Step-by-step explanation:
We are given that line MN and line OP are parallel.
We are also given that ∠OST = 73
Given this we want to find the measure of ∠MTS and ∠STN
∠MTS and ∠OST are supplementary angles
Supplementary angles add up to equal 180°
This means that ∠MTS + ∠OST = 180 ( we can use this equation to solve for the measure of ∠MTS )
∠MTS + ∠OST = 180
∠OST = 73
∠MTS + 73 = 180
subtract 73 from both sides
∠MTS = 107
∠STN and ∠OTS are alternate interior angles.
Alternate interior angles are congruent ( equal to each other )
This means that ∠STN = ∠OTS
Because ∠OTS = 73 and ∠STN = ∠OTS , ∠STN = 73°
In conclusion, ∠MTS = 107 and ∠STN = 73
Therefore the answer is B
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