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vesna_86 [32]
3 years ago
11

In the diagram below, we have ST parallel to QR. angle P= 40 degrees, and angle Q= 35 degrees. Find the measure of angles STR in

degrees.

Mathematics
2 answers:
Drupady [299]3 years ago
7 0

Answer:

m\angle S = 35^\circ, \ m\angle T = 105^\circ,\ m\angle R = 105^\circ

Step-by-step explanation:

<u>Similar Triangles</u>

Lines ST and QR are parallel. Thus, angles S and Q are congruent, and angles T and R are congruent.

Considering the triangle PQR, the sum of its internal angles must be 180°:

m\angle P + m\angle Q + m\angle R = 180^\circ

Substituting the known values:

40^\circ + 35^\circ + m\angle R = 180^\circ

Solving for R:

m\angle R = 180^\circ - 40^\circ - 35^\circ

m\angle R = 105^\circ

Angles S and Q are congruent, thus

m\angle S = 35^\circ

Angles T and R are congruent, thus

m\angle T = 105^\circ

Summarizing:

\mathbf{m\angle S = 35^\circ, \ m\angle T = 105^\circ,\ m\angle R = 105^\circ}

Minchanka [31]3 years ago
5 0

Answer:

100

Step-by-step explanation:

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