Question

in the given figure the measure of angle ABC is?​

Answer 1

Given:

in the given figure the measure of angle ABC is?​

Solution:

Know that the exterior angle theorem of a triangle states that the exterior angle of a triangle is equal to the sum of the other two triangles.

Refer the question image,

$\[\angle A + \angle B = 100^\circ \]$

$\[\begin{array}{l} \Rightarrow \angle C = 180^\circ - 100^\circ \\ \Rightarrow \angle C = 80^\circ \end{array}\]$

check the options,

Since $\[AB \ne AC\]$

Therefore  $\[\angle ABC\]$ will not be equal to $\[80^\circ \]$

Therefore the possible value of $\[\angle ABC = 60^\circ \]$.

Hence, the correct answer is option (d)

Answer 2

Answer:

in the given figure the measure of angle ABC is?

Solution:

Know that the exterior angle theorem of a triangle states that the exterior angle of a triangle is equal to the sum of the other two triangles.

Refer the question image,

\angle A + \angle B = 100^\circ∠A+∠B=100

∘

\begin{gathered}\begin{array}{l} \Rightarrow \angle C = 180^\circ - 100^\circ \\ \Rightarrow \angle C = 80^\circ \end{array}\end{gathered}

⇒∠C=180

∘

−100

∘

⇒∠C=80

∘

check the options,

Since AB \ne ACAB



=AC

Therefore \angle ABC∠ABC will not be equal to 80^\circ80

∘

Therefore the possible value of \angle ABC = 60^\circ∠ABC=60

∘

.

Hence, the correct answer is option (d)