Question

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, find angle P

Answer 1

To find the measure of angle P, set up equations based on the properties of supplementary angles. Solve for Q first, then use it to calculate P, which is found to be 143 degrees.

Step-by-step explanation:

To solve for angle P given that it is supplementary to angle Q, and that its measure is five less than four times the measure of Q, we can set up the following equations based on the properties of supplementary angles:

Let's denote angle P as P and angle Q as Q.

1. P + Q = 180° (since they are supplementary).
2. P = 4Q - 5 (as given in the problem statement).

We can substitute the second equation into the first to find Q:

1. 4Q - 5 + Q = 180º
2. 5Q - 5 = 180º
3. 5Q = 185º
4. Q = 37º

Now we can use the value of Q to find P:

1. P = 4 * 37º - 5
2. 
   
3. P = 148º - 5
4. P = 143º

Therefore, the measure of angle P is 143 degrees.

Answer 2

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.

`(5m\angle Q)/(5)=(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)