Studdy AI Logo
Math

QuestionFind the value of 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, which means their measures add up to90 degrees. . 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, we can set up an equation where the sum of the measures of these two angles equals90 degrees.
m<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

Add to both sides of the equation to isolate the term with x on one side.
16x=9616x =96

STEP 6

Divide both sides of the equation by16 to solve for x.
x=96/16x =96 /16

STEP 7

Calculate the value of x.
x=6x =6

STEP 8

Now that we have the value of x, we can substitute it into the expression for the measure of angle R to find its measure.
m<R=x−7m<R =x -7

STEP 9

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

STEP 10

Calculate the measure of angle R.
m<R=54−7=47m<R =54 -7 =47The solution isx=6x =6m<R=47m<R =47

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord