17. In the given fig, PR || UV and PQ|| RS,
ZRST=30° STU=45º. Find the value
of LQPR+TUV?
नीचे दिए गए चित्र में,PR || UV और PQ || RS
ZRST=30°, ZSTU=45°at
LOPR+LTUV का मान क्या होगा।
R
a)180°
b)195°
c)205
d)165
Answers
Given : PR || UV and PQ|| RS
∠RST=30° ∠STU=45º.
To Find : the value of ∠QPR+∠TUV
a)180°
b)195°
c)205
d)165
Solution:
Extend PR and UV such that it cut transversal ST at A and B
then ∠RAS = ∠UBT = x ( alternate exterior angle )
as PR || UV
∠TUV = x + 45° ( exterior angle of triangle = sum of opposite interior angles )
∠PRS = x + 30° ( exterior angle of triangle = sum of opposite interior angles )
∠PRS + ∠QPR = 180° Interior angles are supplementary. as PQ|| RS,
=> ∠PRS = 180° - ∠QPR
=> 180° - ∠QPR = x + 30°
=> ∠QPR = 150° - x
∠TUV = x + 45°
∠QPR = 150° - x
Adding both
∠QPR + ∠TUV = 150° - x + x + 45°
=> ∠QPR + ∠TUV = 195°
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Interior angles are supplementary. ( adds up to 180°)
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Step-by-step explanation:
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