Question

For the given diagram, the value of ∠QBC is

• A. 50°
• B. 40°
• C. 60°
• D. 70°

Answer 1

The correct option is A 50°

For the diagram shown:


∠PAB = 160° and ∠ACR = 150°

∠PAB and ∠BAC are pair of adjacent angles lying on the straight line PC.
So, they form a linear pair.

So, ∠PAB + ∠BAC = 180°
⇒ ∠BAC + 160° = 180°
⇒ ∠BAC = 180° - 160°
⇒ ∠BAC = 20°

Again,
∠ACR and ∠ACB are pair of adjacent angles lying on the straight line RB.
So, they form a linear pair.

So, ∠ACR + ∠ACB = 180°
⇒ ∠ACB + 150° = 180°
⇒ ∠ACB = 180° - 150°
⇒ ∠ACB = 30°

Angle sum property of a triangle tells that sum of three angles of a triangle is 180°.

So, in △ABC,
∠ACB + ∠ABC + ∠BAC = 180°
⇒ 30° + ∠ABC + 20° = 180°
⇒ ∠ABC = 180° - 50° = 130°

Again,
∠ABC and ∠CBQ are pair of adjacent angles lying on a straight line AQ.
So, they form a linear pair.

So, ∠QBC + ∠ABC = 180°
⇒ ∠QBC + 100° = 180°
⇒ ∠QBC = 180° - 100°
⇒ ∠QBC = 50°

So, value of ∠QBC is 50°.

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