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`.

Answer 1

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°.