In $Δ A B C$ , point D and E lies on the line AB and AC respectively as shown in the figure. Find the measure of $∠ A E D$ .

$65^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$40^{\circ}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$75^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$70^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
$40^{\circ}$

$In Δ A B C,$

$\frac{A D}{D B} = \frac{4}{3} and \frac{A E}{E C} = \frac{4.8}{3.6} = \frac{4}{3}$

$∴ \frac{A D}{D B} = \frac{A E}{E C} = \frac{4}{3}$

We know that in a triangle, if a line segment intersects two sides and divides them in the same ratio, then it will be parallel to the third side.

$∴$ DE || BC

$So, ∠ A E D = ∠ A C B = 40^{\circ}$
$(Corresponding angles are equal)$

Suggest Corrections

Similar questions

In $Δ A B C$ , point D and E lies on the line AB and AC respectively as shown in the figure. Find the measure of $∠ A E D$ .

Δ A B C

∠ A E D

Δ A B C

∠ A E D

Question 41

In $Δ A B C$ , $∠ A = 50^{\circ}, ∠ B = 70^{\circ}$ and bisector of $∠ C$ meets AB at D as shown in the given figure. Measure of $∠ A D C$ is

a) $50^{\circ}$
b) $100^{\circ}$
c) $30^{\circ}$
d) $70^{\circ}$

Δ A B C

∠ B A C = 40^{\circ}

∠ A B C = 65^{\circ}

∠ C E D

Join BYJU'S Learning Program