10 pt question

meg constructed triangle poq and then used a compass and straightedge to accurately construct line segment os, as shown in the figure below:

which could be the measures of angle pos and angle poq?

a. measure of angle pos is 25 degrees, measure of angle poq is 40 degrees
b. measure of angle pos is 25 degrees, measure of angle poq is 30 degrees
c. measure of angle pos is 20 degrees, measure of angle poq is 40 degrees
d. measure of angle pos is 20 degrees, measure of angle poq is 30 degrees

The correct option is c.

Step-by-step explanation:

It is given that Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS.

From the given figure it is clear that OS is angle bisector of POQ,

          (Definition of angle bisector)

It means angle POQ is twice of angle POS.

In option A, the measure of angle POS is 25 degrees, measure of angle POQ is 40 degrees.

In option B, the measure of angle POS is 25 degrees, measure of angle POQ is 30 degrees.

In option D, the measure of angle POS is 20 degrees, measure of angle POQ is 30 degrees.

In options A, B and D, the measure of angle POQ is not twice of angle POS.

In option C, the measure of angle POS is 20 degrees, measure of angle POQ is 40 degrees

Here the measure of angle POQ is twice of angle POS. Therefore option c is correct.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11