QuestionFind $m \angle RSQ = 15x - 43$ and $m \angle TSQ = 8x + 18$ if they sum to a right angle.

Studdy Solution

STEP 1

Assumptions1. The measure of angle RSQ is given by the expression $15x -43$ . The measure of angle TSQ is given by the expression $8x +18$
3. These two angles add together to form a right angle, which measures90 degrees

STEP 2

We can start by setting up an equation that represents the fact that the two angles add together to form a right angle. This can be written as $m \angle RSQ + m \angle TSQ =90$

STEP 3

Substitute the given expressions for the measures of the angles into the equation.
$15x -43 +8x +18 =90$

STEP 4

Combine like terms on the left side of the equation.
$23x -25 =90$

STEP 5

Add25 to both sides of the equation to isolate the term with x on the left side.
$23x =115$

STEP 6

Divide both sides of the equation by23 to solve for x.
$x =115 /23$

STEP 7

Calculate the value of x.
$x =5$

STEP 8

Now that we have the value of x, we can substitute it into the expressions for the measures of the angles to find their actual measures.
For $m \angle RSQ$ , the expression is $15x -43$ .
$m \angle RSQ =15x -43$

STEP 9

Substitute the value of x into the expression for $m \angle RSQ$ .
$m \angle RSQ =15*5 -43$

STEP 10

Calculate the measure of $m \angle RSQ$ .
$m \angle RSQ =75 -43 =32$ So, the measure of $m \angle RSQ$ is32 degrees.

STEP 11

For $m \angle TSQ$ , the expression is $8x +18$ .
$m \angle TSQ =8x +18$

STEP 12

Substitute the value of x into the expression for $m \angle TSQ$ .
$m \angle TSQ =8*5 +18$

STEP 13

Calculate the measure of $m \angle TSQ$ .
$m \angle TSQ =40 +18 =58$ So, the measure of $m \angle TSQ$ is58 degrees.
The measures of $m \angle RSQ$ and $m \angle TSQ$ are32 degrees and58 degrees respectively.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms