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Question
In the given figure, ΔLMN is similar to ΔPQR. To find the measure of ∠N, complete the following activity.
Given: ΔLMN ∼ ΔPQR
Since ΔLMN ∼ ΔPQR, therefore, corresponding angles are equal.
So, ∠L ≅ `square`
⇒ ∠L = `square`
We know, the sum of angles of a triangle = `square`
∴ ∠L + ∠M + ∠N = `square`
Substituting the values of ∠L and ∠M in equation (i),
`square` + `square` + ∠N = `square`
∠N + `square` = `square`
∠N = `square` – `square`
∠N = `square`
Hence, the measure of ∠N is `square`.
Solution
Given: ΔLMN ∼ ΔPQR
Since ΔLMN ∼ ΔPQR, therefore, corresponding angles are equal.
So, ∠L ≅ ∠P
⇒ ∠L = 60°
We know, the sum of angles of a triangle = 180°
∴ ∠L + ∠M + ∠N = 180°
Substituting the values of ∠L and ∠M in equation (i),
60° + 60° + ∠N = 180°
∠N + 120° = 180°
∠N = 180° – 120°
∠N = 60°
Hence, the measure of ∠N is 60°.
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