In the given figure- straight lines PQ and RS intersect at O- If the magnitude of - is 3 times that of - then - is equal to-

The correct option is C 45° θ + ϕ = 180^∘ Since, θ = 3ϕ ⇒ 3ϕ + ϕ = 180^∘ ⇒ 4ϕ = 180^∘ ⇒ ϕ = 45^∘ Hence, ∠ϕ = 45^∘ ...

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Standard IX

Mathematics

Parallel Lines with Transversal

In the given ...

Question

In the given figure, straight lines PQ and RS intersect at O. If the magnitude of $θ$ is 3 times that of $ϕ$ , then $∠ ϕ$ is equal to:

30°

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40°

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45°

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60°

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Solution

The correct option is C
45°

$θ + ϕ = 180^{\circ}$

Since, $θ = 3 ϕ$

$\Rightarrow$ $3 ϕ + ϕ = 180^{\circ}$

$\Rightarrow$ $4 ϕ = 180^{\circ}$

$\Rightarrow$ $ϕ = 45^{\circ}$

Hence, $∠ ϕ = 45^{\circ}$

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Similar questions

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In the given figure, straight lines PQ and RS intersect at O. If the magnitude of θ is 3 times that of ϕ, then ∠ϕ is equal to:

The correct option is C 45° θ+ϕ=180∘ Since, θ=3ϕ ⇒ 3ϕ+ϕ=180∘ ⇒ 4ϕ=180∘ ⇒ ϕ=45∘ Hence, ∠ϕ=45∘

In the given figure, straight lines PQ and RS intersect at O. If the magnitude of $θ$ is 3 times that of $ϕ$ , then $∠ ϕ$ is equal to:

The correct option is C
45°

$θ + ϕ = 180^{\circ}$

Since, $θ = 3 ϕ$

$\Rightarrow$ $3 ϕ + ϕ = 180^{\circ}$

$\Rightarrow$ $4 ϕ = 180^{\circ}$

$\Rightarrow$ $ϕ = 45^{\circ}$

Hence, $∠ ϕ = 45^{\circ}$