The correct option is C 90° In Δ BDA, x + x + y = 180^∘ (by angle sum property) Similarly, in Δ BDC,x + x + ∠ BDC = 180^∘ Comparing the two equations, we have ...

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Incentre and Its Construction

Question

Consider the following figure. The value of $y$ is

Data insufficient – the value of x is required

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60°

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45°

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90°

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Solution

The correct option is D
90°

In $Δ B D A$ , $x + x + y = 180^{\circ}$ (by angle sum property)
Similarly, in $Δ B D C$ , $x + x + ∠ B D C$ = $180^{\circ}$
Comparing the two equations, we have $∠ B D C = y$ .
Also, $∠ B D C$ + $∠ B D A$ = $180^{\circ}$ (linear pair)
$⟹ y + y = 180^{\circ}$
$⟹ y = 90^{\circ}$

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Consider the following figure. The value of y is

The correct option is D 90° In ΔBDA, x+x+y=180∘ (by angle sum property) Similarly, in ΔBDC,x+x+∠BDC = 180∘ Comparing the two equations, we have ∠BDC=y. Also, ∠BDC + ∠BDA = 180∘ (linear pair) ⟹y+y=180∘ ⟹y=90∘

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