In Fig. 8.131, if l1 || l2, what is x + y in terms of w and z?
A. 180 – w + z
B. 180 + w – z
C. 180 – w – z
D. 180 + w + z
Answers
Concept :
Consecutive interior angles : The pair of interior angles on the same side of the transversal are called pairs of consecutive interior angles.
Each pair of consecutive interior angles are supplementary.
Given : l1 ‖ l2
From figure :
∠w + ∠x = 180° (Consecutive interior angle)
x = 180° - w ………..(1)
y = z (Alternate angles) ……….(2)
On adding eq (1) and (2), we get :
x + y = 180° – w + z
Hence x + y in terms of w and z is 180° – w + z.
Option (A) 180° – w + z is correct.
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In Fig. 8.130, if l1||l2, what is the value of x?
A. 90°
B. 85°
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In Fig. 8.126, which of the following statements must be true?
(i) a + b = d + c
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Answer: Opt A) 180 – w + z
Step by step explanation:
Given: L1 ∥ L2
To find: x + y in terms of w and z
Solution:
Angle w + Angle x = 180°
[ Interior angles are supplementary ]
Thus,
Angle x = 180° - Angle w ___[eq.1]
Now,
Angle y = Angle z ___[eq.2]
[ Alternate angles are equal ]
Thus, Adding eq.(1) and eq.(2) :
Angle x + Angle y = 180° - Angle w + Angle z
=> x + y = 180° - w + z
Thus, Opt A is the answer.
Final Answer: x + y in terms of w and z is A) x + y = 180° - w + z