ch 6 class 9 maths
ex 6.1 question 6
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Step-by-step explanation:
Given :-
∠ XYZ = 64°
XY produced to point P
To find :-
Draw the figure from the given information and if YQ bisects ∠ ZYP then find ∠ XYQ and reflex ∠ QYP ?
Solution :-
See the above attachment
Given that
∠ XYZ = 64°
XY produced to point P
If YQ bisects ∠ ZYP then
∠ ZYP = ∠ ZYQ + ∠ QYP
and ∠ ZYQ = ∠ QYP
Let ∠ ZYQ = ∠ QYP = X°
Then
∠ ZYP = X°+X° = 2X°
∠ XYZ + ∠ ZYP = 180°
Since they are linear pair
=> 64°+2X° = 180°
=> 2X° = 180°-64°
=> 2X° = 116°
=> X° = 116°/2
=> X° = 58°
∠ ZYQ = ∠ QYP = 58°
∠ ZYP = 2×58° = 116°
∠ XYQ = ∠ XYZ + ∠ ZYQ
=> ∠ XYQ = 64°+58°
=> ∠ XYQ = 122°
and ∠ QYP = 58°
Reflex of ∠ QYP = 180°-58° = 122°
Answer :-
∠ XYQ = 122°
∠ QYP = 58°
Reflex ∠ QYP = 122°
Used formulae:-
- The sum of two adjacent angles is equal to 180° they are called Linear pair.
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