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[tex]\huge\sf\purple{Question}[/tex]
prefer attachment
A)180-y
B)180+y
C)180-2y
D)90+y
Need explanation
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[tex]\huge\sf\purple{Question}[/tex]
prefer attachment
A)180-y
B)180+y
C)180-2y
D)90+y
Need explanation
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Verified answer
Step-by-step explanation:
Given :-
PQ || RS
To find :-
Find the measure of (x+z) ?
Construction :-
Draw a parallel line UV parallel to PQ and RS through T
Extend PQ to X
Extend SR to W
Proof :-
PQ || UV and TQ is a transversal .
We know that
The interior angles on the same side to the transversal are supplementary.
=> < PQT + <VTQ = 180°
=> x+ < VTQ = 180°
=> x +(z/2) = 180° --------(1)
and
UV || SR and TR is a transversal
We know that
Alternative interior angles are equal.
=> <VTR = <WRT
=> z/2 = y -----------(2)
On adding (1)&(2) then
=> x+(z/2)+(z/2) = 180°+y
=> x+(2z/2) = 180°+y
=> x + z = 180°+y
Answer:-
The measure of x+z is 180°+y
Used formulae:-
If two parallel lines Intersected by a transversal then
→ The interior angles on the same side to the transversal are supplementary.
→ Alternative interior angles are equal.