Question

ch 6 class 9 maths
ex 6.1 question 6​

Answer 1

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.

Answer 2

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