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QuestionFind xx if m∠PQR=x+9m \angle PQR = x + 9, m∠SQR=x−3m \angle SQR = x - 3, and m∠PQS=100m \angle PQS = 100.

Studdy Solution

STEP 1

Assumptions1. The measure of angle PQ is100 degrees. The measure of angleQR is x+9 degrees3. The measure of angleQR is x-3 degrees4. The sum of the measures of angles at a point is360 degrees

STEP 2

We know that the sum of the measures of angles at a point is360 degrees. So, we can write the equation asm \angleQR + m \angleQR + m \angle PQ =360

STEP 3

Substitute the given values into the equation.
(x+9)+(x−3)+100=360(x+9) + (x-3) +100 =360

STEP 4

implify the equation by combining like terms.
2x+106=3602x +106 =360

STEP 5

Subtract106 from both sides of the equation to isolate the term with x.
2x=360−1062x =360 -106

STEP 6

Calculate the right side of the equation.
2x=2542x =254

STEP 7

Divide both sides of the equation by2 to solve for x.
x=254/2x =254 /2

STEP 8

Calculate the value of x.
x=127x =127So, the value of x is127 degrees.

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