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In the given figures, find $∠ M L N$ .

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∠ M L N = 60 °

∠ M L N = 50 °

∠ M L N = 65 °

∠ M L N = 40 °

answer is A.

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Detailed Solution

Given figure is,
CBSE Class 10 Answered

From the figure,

∠ A B C = 50 °, ∠ A C B = 70 ° A B = 4.4 cm, A C = 3.6 cm, B C = 4 cm, N L = 9 cm, N M = 10 cm, and M L = 11 cm

.
We have to find

∠ M L N

.
According to the SSS Similarity Criterion, if the sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal, and the two triangles are similar.
Then by using SSS criterion we can check for

Δ A B C

and

Δ L M N

.
In

Δ A B C

and

Δ L M N

B C M N = 410 = 25

A C L N = 3.6 9 = 25

A B M L = 4.4 11 = 25

From above we get,

B C M N = A C L N = A B M L

.
As the side ratios of the two triangles are identical, the corresponding angles will be equal according to the SSS formula.
Therefore,

∠ A = ∠ M L N

.
Then,
On using angle sum property of triangle in

Δ A B C

∠ A + ∠ B + ∠ C = 180 °

∠ A = 180 ° − ∠ B − ∠ C ⇒ ∠ A = 180 ° − 50 ° − 70 ° ⇒ ∠ A = 60 °

Then we get,

∠ M L N = 60 ° ∠ A = ∠ M L N

Hence, option (1) is correct.

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