Question

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.

Answer 1

Answer:

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

Step-by-step explanation:

Similar Triangles

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:

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

Answer 2

Answer:

100

Step-by-step explanation: