Question

in fig.6.42 if lines pq and rs intersect at point T,such that angle PRT=40 degree,angle RPT=95 degree and angle TSQ=75 degree , find angle SQT .
please give correct answer.please please​

Answer 1

Given :

• ∠RPT = 95°
• ∠PRT = 40°
• ∠TSQ = 75°

To Find :

• ∠SQT

Solution :

In Δ PRT :

$\longmapsto\tt{\angle{PRT}+\angle{RPT}+\angle{PTR}=180^{\circ}\:(A.S.P)}$

$\longmapsto\tt{40^{\circ}+95^{\circ}+\angle{PTR}=180^{\circ}}$

$\longmapsto\tt{135^{\circ}+\angle{PTR}=180^{\circ}}$

$\longmapsto\tt{\angle{PTR}=180^{\circ}-135^{\circ}}$

$\longmapsto\tt\bf{\angle{PTR}=45^{\circ}}$

Also ,

$\longmapsto\tt{\angle{STQ}=\angle{PTR}\:(V.O.A)}$

$\longmapsto\tt\bf{\angle{STQ}=45^{\circ}}$

Now ,

$\longmapsto\tt{\angle{TSQ}+\angle{SQT}+\angle{STQ}=180^{\circ}}$

$\longmapsto\tt{75^{\circ}+\angle{SQT}+45^{\circ}=180^{\circ}}$

$\longmapsto\tt{120^{\circ}+\angle{SQT}=180^{\circ}}$

$\longmapsto\tt{\angle{SQT}=180^{\circ}-120^{\circ}}$

$\longmapsto\tt\bf{\angle{SQT}=60^{\circ}}$

Answer 2

${\large{\rm{\underline{Let's \; understand \; the \; question \; 1^{st}}}}}$

◉ This question says that there is a figure given (attachment) in this figure if the lines pq and rs intersect at point T ,such that ∠ PRT = 40° , ∠ RPT = 95° and ∠ TSQ = 75°. We have to find ∠ SQT.

${\large{\rm{\underline{Given \; that}}}}$

⚔ The lines PQ and RS intersect at point T

⚔ ∠ PRT = 40°

⚔ ∠ RPT = 95°

⚔ ∠ TSQ = 75°

${\large{\rm{\underline{To \; find}}}}$

⚔ Measure of ∠ SQT

${\large{\rm{\underline{Solution}}}}$

⚔ Measure of ∠ SQT = 60°

${\large{\rm{\underline{Full \; Solution}}}}$

☑ For the ∆PRT

➨ ∠ PRT + ∠ RPT + ∠ PTR = 180° (A.S.P)

• A.S.P denotes Angle Sum Property

➨ 40° + 95° + ∠ PTR = 180°

➨ 135° + ∠ PTR = 180°

➨ ∠ PTR = 180° - 135°

➨ ∠ PTR = 45°

${\pink{\frak{Hence, \: angle \: PTR \: measure \: 45 \degree}}}$

☑ Now according to the attachment,

➨ ∠ STQ = ∠ PTR (V.O.A)

• V.O.A denotes vertical opposite angles.

Hencefoerth,

➨ ∠ STQ = 45°

${\pink{\frak{Hence, \: angle \: STQ \: measure \: 45 \degree}}}$

☑ Now let us find the measure of ∠ SQT.

➨ ∠ TSQ + ∠ SQT + ∠ STQ = 180° (A.S.P)

• A.S.P denotes Angle Sum Property

➨ 75° + ∠ SQT + 45° = 180°

➨ 120° + ∠ SQT = 180°

➨ ∠ SQT = 180° - 120°

➨ ∠ SQT = 60°

${\pink{\frak{Hence, \: angle \: SQT \: measure \: 60 \degree}}}$