Given:
The diagram.
To find:
(a) [tex]m\angle SQT[/tex]
(b) [tex]m\angle QRW[/tex]
(c) [tex]m\angle PRV[/tex]
Solution:
(a)
If two lines intersect each other at a point, then the vertically opposite angles are equal.
[tex]m\angle SQT = m\angle PQR[/tex] (Vertically opposite angles)
[tex]m\angle SQT = 36^\circ[/tex]
Therefore, the measure of angle SQT is 36 degrees.
(b)
If a transversal line intersect two parallel lines, then the alternate interior angles are equal.
[tex]m\angle QRW = m\angle PQR[/tex] (Alternate interior angles)
[tex]m\angle QRW = 36^\circ[/tex]
Therefore, the measure of angle QRW is 36 degrees.
(c)
It is given that the angles PRV and angle PRQ are congruent.
Let the measures of angle PRV and angle PRQ are x degrees.
[tex]m\angle PRV+m\angle PRQ+m\angle PQR=180^\circ[/tex] (Adjacent interior angles are supplementary)
[tex]x+x+36^\circ=180^\circ[/tex]
[tex]2x=180^\circ -36^\circ[/tex]
[tex]2x=144^\circ[/tex]
Divide both sides by 2.
[tex]x=\dfrac{144^\circ}{2}[/tex]
[tex]x=72^\circ[/tex]
Therefore, the measure of angle PRV is 72 degrees.
