Find $∠ A$ in the figure given below.

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Solution

Given,
In $△ D E F,$
$∠ D = 60 °$
$∠ F = 70 °$

We know that, sum of all the interior angles of a triangle is 180°.

Therefore,
$∠ E = 180 ° - (60 ° + 70 °)$
$∠ E = 50 °$

In $△ A C B and △ D E F$ ,

CB = EF .... (Given)

$∠ C = ∠ E = 50 °$ .... (Given)

AC = DE .... (Given)

So, by SAS criteria for congruency of triangles,
$△ A C B ≅ △ D E F$

Thus,
$∠ A = ∠ D = 60 °$ ... (Corresponding parts of congruent triangles)

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