I need correct answer with step by step
Answers
given- ∠SPR= 135°
∠SQT=110°
find ∠PRQ=
∠SQT+∠PQR=180°(linear pair). ∠ SQT+∠PQR= 180
∠PQR = 180-110
∠PQR= 70°
∠PQR+∠PRQ=∠SQT
70°+∠PRQ= 110°
∠PRQ=110-70
= 40°
Answer:
∠PRQ = 65°
Step-by-step explanation:
From the figure, we have:
=> ∠PQT = 110°
=> ∠SPR = 135°
We are asked to find:
=> ∠PRQ
Solution:
>> In the figure
=> TQR is a straight line
=> ∴ 110° + x° = 180°
=> x° = 70° [∠PQR]
>> In the figure
=> QPS is a straight line
=> ∴ 135° + x° = 180°
=> x° = 45° [∠RPQ]
Now, in ΔPQR,
=> ∠PQR + ∠RPQ + ∠PRQ = 180°
[ ∵ Angle sum property ]
=> 70° + 45° + ∠PRQ = 180°
=> 115° + ∠PRQ = 180°
=> ∠PRQ = 180° - 115°
=> ∠PRQ = 65°
Must know:
Angle sum property: Sum of all the interior angles in a triangle is equal to 180°
Straight line property: From the figure, we observe two straight lines QPS and TQR, when an angle lies on a straight line then the other angle and given angle's sum will be equal to 180°.