Question

In the following figure, find ∠ x and ∠ y, if ∠x – ∠y – 10°

Answer 1

Answer:

a)65,55

Step-by-step explanation:

By Exterior Angle Property

Sum of two interior opposite angles = Exterior Angle

One opposite interior angle= x

Another opposite interior angle=y

According to question

x+y= 120°

If we take x= 65°

and y=55°

then,

x+y= 65°+55°= 120°

Here, d) 60°, 60° cannot be the answer because then both variables would be x and not X and y

Answer 2

To Find :- In the following figure, find ∠ x and ∠ y, if ∠x – ∠y = 10° ?

Concept used :-

• In a triangle exterior angle is equal to sum of opposite interior angles .

Solution :-

Let QR is extended at point S .

given that,

→ ∠x – ∠y = 10° ---------- Equation (1)

and, from above told concept,

→ ∠PQR + ∠QPR = ∠QRS

So,

→ ∠x + ∠y = 120° ---------- Equation (2)

adding Equation (1) and Equation (2) we get,

→ (∠x – ∠y) + (∠x + ∠y) = 10° + 120°

→ ∠x + ∠x - ∠y + ∠y = 130°

→ 2•∠x = 130°

dividing both sides by 2,

→ ∠x = 65°

putting value of ∠x in Equation (1),

→ ∠x - ∠y = 10°

→ 65° - ∠y = 10°

→ ∠y = 65° - 10°

→ ∠y = 55°

therefore, ∠x is equal to 65° and ∠y is equal to 55° .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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