In the diagram below of triangle M, N, OMNO, PP is the midpoint of start overline, M, O, end overline
MO
and QQ is the midpoint of start overline, N, O, end overline
NO
. If mangle, O, N, M, equals, minus, 2, x, plus, 79∠ONM=−2x+79, and mangle, O, Q, P, equals, 6, x, plus, 63∠OQP=6x+63, what is the measure of angle, O, N, M∠ONM?
To find the measure of angle ONM, we can set up an equation using the fact that the sum of the interior angles of a triangle is always 180 degrees.
From the given information, we know that angle ONM is equal to -2x + 79 and angle OQP is equal to 6x + 63. Since PP is the midpoint of MO and QQ is the midpoint of NO, we can also determine that angle OMP is equal to angle NMQ (since PP and QQ are parallel).
Let's call the measure of angle OMP (or angle NMQ) y degrees. Then, we can set up an equation as follows:
-2x + 79 + y + y = 180
-2x + 79 + 2y = 180
Similarly, we know that angle OQP is supplementary to angle NMQ (since QQ and MO are parallel), so we can set up another equation:
6x + 63 + y = 180
Now we have a system of two equations:
1. -2x + 79 + 2y = 180
2. 6x + 63 + y = 180
Solving this system of equations will give us the values of x and y. Subsequently, plug in the value of x to find the measure of angle ONM.