Question

Find m∠P in the diagram.

Answer 1

Firstly, lines SR and PQ are parallel, right?

Answer 2

yes

Answer 3

Angle S and angle P, they are interior angles on the same side, right?
What do we know about interior angles on the same side?

Answer 4

they have the same angle so its 50 degree

Answer 5

No :)
Intuitively, do they LOOK like they have the same angle? Angle P looks obtuse while Angle S looks acute...

Answer 6

Actually, angle S IS acute, as it measures 50 degrees.
But that's not the correct way to look at it.

Same-Side Interior angles are SUPPLEMENTARY if the lines associated with them are parallel.

Answer 7

so its that twice the degree

Answer 8

No. What does supplementary mean?
Two angles are supplementary if they....?

Answer 9

they add up to 180 degree

Answer 10

That's right. So angle S and angle P must add up to 180 degrees...
m∠S + m∠P = 180
m∠S = 50
Now just solve for m∠P

Answer 11

130 degree

Answer 12

And you're done.

Answer 13

thank you for the help

Answer 14

No problem