Question

Two lines PQ and RS intersect at a point O. If angle POR = 35°, find the measure of angle SOQ, ANGLE ROQ, AND POS.

Answer 1

To find the measure of angle SOQ, we first need to find the measure of angle ROQ. Angle ROQ is also 35°. Now, to find the measure of angle SOQ, we can subtract the measures of angles ROQ and POR from 360°: 360° - 35° - 35° = 290°. Finally, to find the measure of angle POS, we can use the fact that angles that are on the same side of a transversal and are formed by intersecting lines are supplementary.

Step-by-step explanation:

To find the measure of angle SOQ, we first need to find the measure of angle ROQ. Angle ROQ is an opposite angle to angle POR because they are formed by intersecting lines and are on opposite sides of the transversal. Therefore, angle ROQ is also 35°.

Now, to find the measure of angle SOQ, we can use the fact that the sum of the measures of the angles around a point is 360°. The measure of angle SOQ can be found by subtracting the measures of angles ROQ and POR from 360°: 360° - 35° - 35° = 290°.

Finally, to find the measure of angle POS, we can use the fact that angles that are on the same side of a transversal and are formed by intersecting lines are supplementary. Since angle POR is 35°, angle POS is 180° - 35° = 145°.