Question

If ABC is an isosceles triangle with $AB=AC$ and $\angle BAC=70^\circ$, then the external angle at C is

• A. $55^\circ$
• B. $125^\circ$
• C. $110^\circ$
• D. $140^\circ$

Hint:

Exterior angle = $180^\circ -$ adjacent interior angle.

Answer 1

The Correct Option is B

Concept: In an isosceles triangle, angles opposite equal sides are equal.

Step 1: Find the interior angle at C.
Since \[ AB=AC \] the base angles are equal. Let \[ \angle B=\angle C=x \] Using the angle sum property, \[ 70^\circ+x+x=180^\circ \] \[ 2x=110^\circ \] \[ x=55^\circ \] Therefore, \[ \angle C=55^\circ \]

Step 2: Calculate the exterior angle.
Exterior angle and interior angle form a linear pair. \[ \text{Exterior angle at C} = 180^\circ-55^\circ \] \[ =125^\circ \]