Answer :
Answer: 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°
The measure of m ∠PQR is 134 degrees.
Given
PS is a line segment.
Q is the point between segment PS.
QR is another line segment that passes through segment PS.
Which property of the triangle is used to solve the value of x?
The sum of two angles made on one line is equal to 180 degrees.
[tex]\angle \rm PQR + \angle SQR = 180[/tex]
Where the angle QPR is (3x + 5) degree and angle SQR is (x + 3) degree.
Substitute all the values in the equation
[tex]\angle \rm PQR + \angle SQR = 180\\\\(3x+5) + (x+3) =180\\\\3x+5+x+3=180\\\\4x+8=180\\\\4x=180-8\\\\4x=172\\\\x = \dfrac{172}{4}\\\\x =43[/tex]
The value of x is 43 degrees.
Therefore,
The measure of m ∠PQR is;
[tex]\rm m \angle PQR = 3x+5 = 3(43) + 5= 129+5=134[/tex]
Hence, the measure of m ∠PQR is 134 degrees.
To know more about the Properties of triangles click the link given below.
https://brainly.com/question/9404288