In figure- if QT - PR - - TQR -40- and - SPR -50- find the sum of angles x and y-A- 110B- 120C- 130D- 150

The correct option is D 150 In ΔTQR, 90^∘ + 40^∘ + ∠x = 180^∘ (Angle Sum property) Therefore ∠x = 50^∘ Now ∠y = ∠SPR + ∠x ∠y = 50^∘ + 50^∘ = 180^∘ Now ∠x + ∠y ...

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Byju's Answer

Standard IX

Mathematics

Side Lengths

In figure, if...

Question

In figure, if QT $⊥$ PR, $∠$ TQR = $40^{\circ}$ , and $∠$ SPR = $50^{\circ}$ , find the sum of angles x and y.

110

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120

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130

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150

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Solution

The correct option is D
150

In $Δ$ TQR, $90^{\circ}$ + $40^{\circ}$ + $∠$ x = $180^{\circ}$ (Angle Sum property)

Therefore $∠$ x = $50^{\circ}$

Now $∠$ y = $∠$ SPR + $∠$ x

$∠$ y = $50^{\circ}$ + $50^{\circ}$ = $180^{\circ}$

Now $∠$ x + $∠$ y = $50^{\circ}$ + $100^{\circ}$ = $150^{\circ}$

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In figure, if QT ⊥ PR, ∠TQR = 40∘, and ∠SPR = 50∘, find the sum of angles x and y.

The correct option is D 150 In ΔTQR, 90∘ + 40∘ + ∠x = 180∘ (Angle Sum property) Therefore ∠x = 50∘ Now ∠y = ∠SPR + ∠x ∠y = 50∘ + 50∘ = 180∘ Now ∠x + ∠y = 50∘ + 100∘ = 150∘

In figure, if QT $⊥$ PR, $∠$ TQR = $40^{\circ}$ , and $∠$ SPR = $50^{\circ}$ , find the sum of angles x and y.