Two parallel lines are intersect by the same line, and the angles shown lie on the same orientation about the intersection so the angles are equal to each other...which means:
9x+21=10x+10 subtract 21 from both sides
9x=10x-11 subtract 10x from both sides
-x=-11 divide both sides by -1
x=11
You know that the two angles make up a perfectly flat line, which is a 180<span>° angle. So we can create the equation:'
3x + 10 = 12x
Now solve for 'x'. Subtract 3x to both sides:
10 = 9x
Divide 9 to both sides:
x = 10/9
We want to find the smaller angle, so put this value in for 'x' in '3x + 10':
3x + 10
3(10/9) + 10
30/9 + 10
13 1/3</span><span>°</span>
Your answers are ...
1) <span>Arc PQ is congruent to arc SR.
2) </span>The measure of arc QR is 150°.
4) <span>Arc PS measures about 13.1 cm.
5) </span><span>Arc QS measures about 15.7 cm.
All of them are correct except for the third answer...
Hope this helps!</span>
Answer:
Step-by-step explanation:
