angle ABD and angle ACE are exterior angles o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) In $\Delta ABC$,the exterior angle at vertex $B$ is $\angle ABD = 140^{\circ}$. Since the sum of an interior angle and its adjacent exterior angle

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(D) In $\Delta ABC$,the exterior angle at vertex $B$ is $\angle ABD = 140^{\circ}$. Since the sum of an interior angle and its adjacent exterior angle is $180^{\circ}$,we have $\angle ABC = 180^{\circ} - 140^{\circ} = 40^{\circ}$.Similarly,the exterior angle at vertex $C$ is $\angle ACE = 80^{\circ}$. Thus,the interior angle $\angle ACB = 180^{\circ} - 80^{\circ} = 100^{\circ}$.In $\Delta ABC$,the sum of all interior angles is $180^{\circ}$. Therefore,$\angle A + \angle ABC + \angle ACB = 180^{\circ}$.Substituting the values,$\angle A + 40^{\circ} + 100^{\circ} = 180^{\circ}$.$\angle A + 140^{\circ} = 180^{\circ}$.$\angle A = 180^{\circ} - 140^{\circ} = 40^{\circ}$.

$\angle ABD$ and $\angle ACE$ are exterior angles of $\Delta ABC$. If $\angle ABD = 140^{\circ}$ and $\angle ACE = 80^{\circ}$,then find $\angle A$. (in $^{\circ}$)

Similar Questions

In the given figure,if $AB \parallel CD$,$\angle AXY = 80^{\circ}$ and $\angle XZD = 140^{\circ}$,then find $x$ and $y$.

In the figure,$x=y$ and $a=b$. Prove that $l \parallel n$.

If two lines intersect,prove that the vertically opposite angles are equal.

State whether the following statement is true or false:
$(1)$ In $\Delta PQR$,$\angle P = \angle Q = 95^{\circ}$ is possible.

Find the measure of the complementary angle of an angle of $44^{\circ}$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module