What is m∠PQR? The PS is line segment. Q is the point between segments PS. QR is another line segment passes through segment PS. The angle PQR is (3x + 5) degree and angle SQR is (x + 3) degree.

The measure of m ∠PQR is 134 degrees.

PS is a line segment.

Q is the point between segment PS.

QR is another line segment that passes through segment PS.

The sum of two angles made on one line is equal to 180 degrees.

Where the angle QPR is (3x + 5) degree and angle SQR is (x + 3) degree.

Substitute all the values in the equation

The value of x is 43 degrees.

Therefore,

The measure of m ∠PQR is;

Hence, the measure of m ∠PQR is 134 degrees.

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m∠PQR = 134°

Step-by-step explanation:

Given:  PS is line segment. Q is the point between segment PS. QR is another line segment passes through segment PS.

That means ∠PQR and ∠SQR are linear pair  [Linear pair is a pair of two angles made on one line and their sum is 180°]

⇒  ∠PQR +  ∠SQR  = 180°  (i)

Since, ∠PQR is (3x + 5)° and ∠ SQR is (x + 3)°   [given]

Put this in (i), we get

(3x + 5)° + (x + 3)° = 180°

⇒ 3x + 5 + x + 3 = 180

⇒ 4 x + 8 = 180

⇒ 4 x = 180-8

⇒ 4 x = 172

Divide both sides by 4

⇒  x= 43

So,  ∠PQR=  (3(43) + 5)° = 134°

Hence, m∠PQR = 134°

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