If qs bisects pat, sqt= (8x-25), pqt=(9x+34) and sqr= 112 find each measure

Angles shown: PQS, SQT, TQR, PQR

For sake of ease, I’ll solve the angles in this order:

1. SQT

2. PQS

3. TQR

4. PQR

If Ray QS bisects angle PQT

Then, m∠PQT = m∠SQT + m∠PQS

And m∠SQT = m∠PQS

Therefore, m∠PQT = 2m∠SQT = 2m∠PQS

1. Find the measure of angle SQT

Given,

m∠SQT = (8x-25)

m∠ PQT= (9x+34)

Since m∠PQT = 2m∠SQT

9x + 34 = 2 (8x – 25)

9x + 34 = 16x – 50

Add 50 to both sides of the equation

9x + 34 + 50 = 16x – 50 + 50

9x + 84 = 16x

Subtract 9x from both sides of the equation

9x – 9x + 84 = 16x – 9x

84 = 7x

7x = 84

x = 84/7

x = 12

m∠SQT = (8x-25)

m∠SQT = (8*12) – 25

m∠SQT = 96 – 25

m∠SQT = 71

2. Find the measure of angle PQS

m∠SQT = m∠PQS

m∠SQT = 71

Therefore, m∠PQS = 71

3. Find the measure of angle TQR

m∠SQR = m∠SQT + m∠TQR

m∠TQR = m∠SQR – m∠SQT

Given,

m∠SQR=112

m∠SQT = 71

m∠TQR = 112 – 71

m∠TQR = 41

4. Find the measure of angle PQR

m∠SQT + m∠ PQS + m∠ TQR + m∠ PQR = 360

m∠SQT = 71

m∠PQS = 71

m∠TQR = 41

Therefore, 71 + 71 + 41 + m∠ PQR = 360

183 + m∠ PQR = 360

Subtract 183 from both sides of the equation

183 – 183 + m∠ PQR = 360 -183

m∠ PQR = 360 -183

m∠ PQR = 177

Conclusively, each measure is as stated below:

1. m∠SQT = 71

2. m∠PQS = 71

3. m∠TQR = 41

4. m∠PQR = 177

the 4th choice is the correct one

step-by-step explanation:

the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

every act of terrorism of islamic sects is done “in the name of allah”. that justifies their actions. islam people who commit those terrorist attacks are not afraid to die. that is why the attacks have horrible consequences. they know they are going to die and they are proud to do it because it is in the name of allah, so it is justified and is for a “good cause.”

since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.