Name: Lines and Angles
Uploaded: 2019-07-19
Duration: 14 min 11 s
Description: Watch this educative video to learn about the different kinds of angles formed when two parallel lines are intersected by a third line.

Question

In the given figure, if $P Q ∥ S T, ∠ P Q R = 110 °$ and $∠ R S T = 130 °,$ find $∠ Q R S .$

Accepted Answer

Given: $P Q ∥ S T, ∠ P Q R = 110 °$ and $∠ R S T = 130 °$ .

Construction: Let us draw a line $X Y$ parallel to $S T$ and passing through point $R .$

Now, $∠ P Q R + ∠ Q R X = 180 °$ (co-interior angles on the same side of transversal $Q R$ )

$\Rightarrow 110 ° + ∠ Q R X = 180 °$

$\Rightarrow ∠ Q R X = 180 ° - 110 °$

$\Rightarrow ∠ Q R X = 70 °$

Also, $∠ R S T + ∠ S R Y = 180 °$ (co-interior angles on the same side of transversal $S R$ )

$\Rightarrow 130 ° + ∠ S R Y = 180 °$

$\Rightarrow ∠ S R Y = 50 °$

$∠ X R Y$ is a straight angle. $R Q$ and $R S$ stand on it.

Therefore, $∠ Q R X + ∠ Q R S + ∠ S R Y = 180 °$

$\Rightarrow 70 ° + ∠ Q R S + 50 ° = 180 °$

$\Rightarrow ∠ Q R S = 180 ° - 120 °$

$\Rightarrow ∠ Q R S = 60 °$

Hence, the value of $∠ Q R S$ is $60 °$ .

Goa Board Solutions for Chapter: Lines and Angles, Exercise 2: EXERCISE

Goa Board Mathematics Solutions for Exercise - Goa Board Solutions for Chapter: Lines and Angles, Exercise 2: EXERCISE

Questions from Goa Board Solutions for Chapter: Lines and Angles, Exercise 2: EXERCISE with Hints & Solutions

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