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QuestionFind the measures of angles ∠P\angle P and ∠Q\angle Q if ∠P=2∠Q−3\angle P = 2\angle Q - 3 and they are supplementary.

Studdy Solution

STEP 1

Assumptions1. The measure of angle is three less than twice the measure of angle Q. This can be written as m∠=m∠Q−3m\angle =m\angle Q -3. . Angle and angle Q are supplementary angles. This means that their measures add up to180 degrees, or m∠+m∠Q=180m\angle + m\angle Q =180.

STEP 2

We have two equations and two unknowns (m∠m\angle and m∠Qm\angle Q). We can solve these equations simultaneously. Let's start by substituting m∠m\angle from the first equation into the second equation.
m∠+m∠Q=180m\angle + m\angle Q =180Substitute m∠=2m∠Q−m\angle =2m\angle Q -(2m∠Q−)+m∠Q=180(2m\angle Q -) + m\angle Q =180

STEP 3

implify the equation by combining like terms.
3m∠Q−3=1803m\angle Q -3 =180

STEP 4

Isolate 3m∠Q3m\angle Q by adding3 to both sides of the equation.
3m∠Q=180+33m\angle Q =180 +3

STEP 5

Calculate the right side of the equation.
3m∠Q=1833m\angle Q =183

STEP 6

olve for m∠Qm\angle Q by dividing both sides of the equation by3.
m∠Q=183/3m\angle Q =183 /3

STEP 7

Calculate the measure of angle Q.
m∠Q=183/3=61m\angle Q =183 /3 =61

STEP 8

Now that we have the measure of angle Q, we can find the measure of angle by substituting m∠Q=61m\angle Q =61 into the first equation.
m∠=2m∠Q−3m\angle =2m\angle Q -3Substitute m∠Q=61m\angle Q =61m∠=2(61)−3m\angle =2(61) -3

STEP 9

Calculate the measure of angle.
m∠=2(61)−3=119m\angle =2(61) -3 =119The measures of angle and angle Q are119 degrees and61 degrees, respectively.

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