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2 years ago

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Mathematics

1 answer:

drek231 [11]2 years ago

5 0

a. The value of x is 7

b. The measure of ∠1 is 99°

<h3>Calculating angles </h3>

From the question, we are to solve for x

From the given diagram, we can write that

m∠NMQ + m∠MQN + m∠QNM = 180° (Sum of angles in a triangle)

From the given information,

m∠NMQ = 5x +19

m∠MQN = 8x -11

m∠QNM = 11x + 4

Then,

5x + 19 + 8x -11 + 11x + 4 = 180

Collect like terms

5x + 8x + 11x = 180 - 19 + 11 - 4

24x = 168

∴ x = 168/24

x = 7

Hence, the value of x is 7

b.
Measure of ∠1 + m∠QNM = 180° (Sum of angles on a straight line)

∴ Measure of ∠1 = 180° - m∠QNM

But m∠QNM = 11x + 4

∴ m∠QNM = 11(7) + 4

m∠QNM = 77 + 4

m∠QNM = 81°

Then,

Measure of ∠1 = 180° - 81°

Measure of ∠1 = 99°

Hence, the measure of ∠1 is 99°

Learn more on Calculating angles here: brainly.com/question/25716982

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