Question

↔PR || ↔XY and ↔CD is the transversal, if ∠PGC = 65°, find the measure of the remaining angles.

Answer 1

SOLUTION:-
GIVEN BY:-
PR || XY and CD is transversal.
∠PGC = 65°
then,
∠CGR = 180 - 65 = 115
∠CGR = ∠PGK = 115
∠PGK = ∠XKD = 115
∠XKD = ∠GKY = 115
and
∠PGC = ∠RGK = 65
∠RGK = ∠YKD = 65
∠YKD = ∠GKD = 65

■I HOPE ITS HELP■

Answer 2

It is given that ,

PR // XY , CD is the transversal ,

<1 = 65° ( given )

i ) <1 = <3 = 65°

[ vertically opposite angles]

ii ) <1 + <2 = 180° [ linear pair ]

65° + <2 = 180

=> <2 = 180 - 65

=> <2 = 115°

iii ) <2 = <4 = 115 °

[ vertically opposite angles ]

iv ) <1 = <5 [ corresponding angles ]

v ) <5 = <7

[ vertically opposite angles ]

vi ) <2 = <6

[ corresponding angles ]

vii ) <6 = <7

[ vertically opposite angles ]

Therefore ,

<1 = <3 = <5 = <7 = 65°

<2 = <4 = <6 = <8 = 115°

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