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Tju [1.3M]
3 years ago
13

The measure of angle P is five less than four times the measure of angle Q. Of angle P and angle Q are supplementary angles, fin

d angle P
Mathematics
1 answer:
Andru [333]3 years ago
7 0

Answer:

m∠P=140°

Step-by-step explanation:

Given:

∠P and ∠Q are supplementary angles.

The measure of angle P is five less than four times the measure of angle Q.

To find m∠P

Solution:

The measure of angle P can be given as:

A) m\angle P=4(m\angle Q-5)

And

B) m\angle P+ m\angle Q=180 [Definition of supplementary angles]

Substituting equation A into B.

4(m\angle Q-5)+ m\angle Q=180

Solving for m\angle Q

Using distribution:

4m\angle Q-20+ m\angle Q=180

Simplifying by combining like terms.

5m\angle Q-20=180

Adding 20 to both sides.

5m\angle Q-20+20=180+20

5m\angle Q=200

Dividing both sides by 5.

\frac{5m\angle Q}{5}=\frac{200}{5}

m\angle Q=40

Substituting m\angle Q=40 in equation B.

m\angle P+ 40=180

Subtracting both sides by 40.

m\angle P+ 40-40=180-40

m\angle P=140

Thus, we have:

m∠P=140° (Answer)

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