Question

In the following figure D and E are points on side AB and AC of triangle ABC respectively such that DE||BC If angle B = 30 and A =40 find x,y and z

Answer 1

Given:

In the given figure, D and E are points lying on AB and AC if  ΔABC such that DE||BC.

∠B=30° and ∠A=40°

To Find:

$x=?$

$y=?$

$z=?$

Solution:

In ΔABC, ∠A=40° and ∠B=30°.

From the angle sum property of a triangle, we know that the sum of the interior angles of a triangle is equal to 180°.

   ∠A+∠B+∠C=180°

⇒ 30°+40°+$x$=180°

⇒ $x=$ 180°-30°-40°

⇒ $x=$ 110°

Here DE||BC and DB and EC are transversals.

When lines are parallel, corresponding angles are equal.

⇒ $x=$ ∠B = 30° and $z=$ ∠C =110°.

Hence, we found $x=$ 30°, $y=$ 110° and $z=$ 110°.