SOLUTION: Given: < MOR=(3x-7)degrees < ROP=(4x-1) Segment MO is perpendicular to segment OP Which angle is larger, < MOR or

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Question 1122928: Given: < MOR=(3x-7)degrees
< ROP=(4x-1)
Segment MO is perpendicular to segment OP
Which angle is larger, < MOR or < ROP?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
This is likely how the drawing looks. The location of point R isn't important as long as it's somewhere between MO and OP, and that segment MO is perpendicular to segment OP. This means MO and OP form a 90 degree angle.

(drawing not to scale)

Note how angle MOR and angle ROP are pieces that combine to form angle MOP, which is 90 degrees. Therefore
(angle MOR) + (angle ROP) = angle MOP
(angle MOR) + (angle ROP) = 90 degrees
(3x-7) + (4x-1) = 90
3x-7 + 4x-1 = 90
(3x+4x)+(-7-1) = 90
7x-8 = 90
7x-8+8 = 90+8
7x = 98
7x/7 = 98/7
x = 14

now that we know x = 14, we can use this to find the measure of each angle
Angle MOR = (3x-7) degrees
Angle MOR = (3*14-7) degrees
Angle MOR = (42-7) degrees
Angle MOR = 35 degrees

Angle ROP = (4x-1) degrees
Angle ROP = (4*14-1) degrees
Angle ROP = (56-1) degrees
Angle ROP = 55 degrees

Note how 35+55 = 90 which helps confirm we have the right angle values.
We see that Angle ROP is the larger angle

SOLUTION: Given: < MOR=(3x-7)degrees < ROP=(4x-1) Segment MO is perpendicular to segment OP Which angle is larger, < MOR or < ROP?