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QuestionFind xx if angles <R<R and <S<S are complementary with m<R=(9x−7)m<R=(9x-7) and m<S=(7x+1)m<S=(7x+1).

Studdy Solution

STEP 1

Assumptions1. Angles R and are complementary angles. . The measure of angle R is given by the expression (9x−7)(9x -7).
3. The measure of angle is given by the expression (7x+1)(7x +1).

STEP 2

Since angles R and are complementary, the sum of their measures is90 degrees. We can express this as an equationm<R+m<S=90m<R + m<S =90

STEP 3

Substitute the given expressions for the measures of angles R and into the equation.
(9x−7)+(7x+1)=90(9x -7) + (7x +1) =90

STEP 4

implify the left side of the equation by combining like terms.
16x−6=9016x -6 =90

STEP 5

To isolate the variable x, first add to both sides of the equation.
16x−+=90+16x - + =90 +

STEP 6

implify both sides of the equation.
16x=9616x =96

STEP 7

Finally, divide both sides of the equation by16 to solve for x.
x=9616x = \frac{96}{16}

STEP 8

Calculate the value of x.
x=9616=6x = \frac{96}{16} =6

STEP 9

Now that we have the value of x, we can find the measure of angle R. Substitute x =6 into the expression for m
m<R=9x−7m<R =9x -7

STEP 10

Substitute x =6 into the equation.
m<R=9(6)−7m<R =9(6) -7

STEP 11

Calculate the measure of angle R.
m<R=9(6)−7=54−7=47m<R =9(6) -7 =54 -7 =47So, x =6 and the measure of angle R is47 degrees.

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