. If QS bisects angle PQR, m angle PQS = (7x - 6)° , and m angle SQR = (4x + 15)° , find m angle PQT.

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KurdishPotato KurdishPotato · Answer 1 · 2021-07-09T22:10:07+02:00

Answer:

94

Step-by-step explanation:

PQS = (7x - 6)°

SQR = (4x + 15)° since QS bisect PQR these two expressions must be equal

so

7x - 6 = 4x + 15 transfer like terms to the same side of the equation

7x - 4x = 15 + 6

3x = 21 divide both sides by 3

x = 7

also the sum of these two would give us the measure of PQR

7x + 4x + 15 - 6 = PQR

11x + 9 = PQR replace x with 7

11*7 + 9 = 86 this is the measure of angle PQR and also supplementary to PQT so the measure of PQT = 180 - 86

lisboa lisboa · Answer 2 · 2021-09-15T01:48:00+02:00

If QS bisects angle PQR. the m<PQT=94 °

Given :

Measure of angles PQS = (7x - 6)° , and m angle SQR = (4x + 15)°

QS bisects angle PQR. So m<PQS=m<SQR

[tex]7x-6=4x+15\\Solve \; for \; x\\7x-4x-6=15\\3x-6=15\\3x=15+6\\3x=21\\divide \; by \;3 \\x=7[/tex]

Now we find out m<PQR

[tex]m<PQR=m<PQS+m<SQR\\m<PQR=7x-6+4x+14\\m<PQR=11x+8\\x=7\\m<PQR=11(7)+8=85[/tex]

We know that <PQR and <PQT are linear pair of angles

The sum of linear pair of angles are supplementary

[tex]m<PQR+m<PQT=180\\86+m<PQT=180\\m<PQT=180-86\\m<PQT=94[/tex]

Learn more : brainly.com/question/617412