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QuestionFind ∠QPS\angle \mathrm{QPS} if ∠QPR=6x+6\angle \mathrm{QPR} = 6x + 6 and ∠RPS=2x+4\angle \mathrm{RPS} = 2x + 4.

Studdy Solution

STEP 1

Assumptions1. The measure of ∠QPS\angle \mathrm{QPS} is represented by 6x+66x+6. . The measure of another angle (not specified in the problem) is represented by x+4x+4.
3. The two angles are supplementary, meaning they add up to180 degrees. This assumption is based on the typical problems of this nature in geometry.

STEP 2

First, we need to set up an equation that represents the sum of the two angles. Since they are supplementary, their sum is180 degrees.
6x+6+2x+4=1806x+6 +2x+4 =180

STEP 3

implify the left side of the equation by combining like terms.
8x+10=1808x +10 =180

STEP 4

Subtract10 from both sides of the equation to isolate the term with x.
8x=180−108x =180 -10

STEP 5

Calculate the right side of the equation.
8x=1708x =170

STEP 6

Divide both sides of the equation by8 to solve for x.
x=1708x = \frac{170}{8}

STEP 7

Calculate the value of x.
x=21.25x =21.25

STEP 8

Now that we have the value of x, we can substitute it into the expression for ∠QPS\angle \mathrm{QPS} to find its measure.
∠QPS=6x+6\angle \mathrm{QPS} =6x+6

STEP 9

Substitute the value of x into the expression for ∠QPS\angle \mathrm{QPS}.
∠QPS=6(21.25)+6\angle \mathrm{QPS} =6(21.25) +6

STEP 10

Calculate the measure of ∠QPS\angle \mathrm{QPS}.
∠QPS=127.5+6=133.5\angle \mathrm{QPS} =127.5 +6 =133.5The measure of ∠QPS\angle \mathrm{QPS} is133.5 degrees.

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