The value of x is 7 and the measure of ∠1 is 99
How to solve for x?
The given parameters are:
- ∠NMQ = 5x + 19
- ∠MQN = 8x - 11
- ∠QNM = 11x + 4
The sum of angles in a triangle is 180.
So, we have:
5x + 19 + 8x - 11 + 11x + 4 = 180
Evaluate the like terms
24x = 168
Divide both sides by 24
x = 7
Hence, the value of x is 7
How to determine the measure of ∠1?
The angles on a straight line add up to 180.
This means that:
∠1 + ∠QNM = 180
Subtract ∠QNM from both sides
∠1 = 180 - ∠QNM
Substitute ∠QNM = 11x + 4
∠1 = 180 - 11x - 4
Substitute x = 7
∠1 = 180 - 11 * 7- 4
Evaluate
∠1 = 99
Hence, the measure of ∠1 is 99
Read more about angles at:
https://brainly.com/question/24839702
#SPJ1
