In ΔABC, ∠ A =30°, ∠ B=40° and ∠ C=110°. The angles of the triangle formed by joining the mid-points of the sides of this triangle are

Question

In &#x394;ABC, &#x2220; A =30&#xB0;, &#x2220; B=40&#xB0; and &#x2220; C=110&#xB0;. The angles of the triangle formed by joining the mid-points of the sides of this triangle are

Philoid · Accepted Answer

Given,

In ∆ABC

∠A=30°,∠B=40°,∠C=110°

In figure, BDEF,DCEF,DEAF are parallelograms so,

∠B = ∠E = 40° [∵∠B&∠E are opposite angles of parallelogram BDEF]

∠C=∠F = 110° [ ∵ ∠C &∠F are opposite angles of parallelogram DCEF]

∠A=∠D =30° [ ∵∠A &∠D are opposite angles of parallelogram DEAF]

Hence, ∠D = 30°

∠E = 40°

∠F = 110°

In ΔABC, ∠A =30°, ∠B=40° and ∠C=110°. The angles of the triangle formed by joining the mid-points of the sides of this triangle are