Question

Find the measure of base angles and exterior angle at the vertex of an isosceles triangle if the vertex angle measures ${45}^o$.

• A. Base angle $={67.5}^o$, exterior angle $={135}^o$
• B. Base angle $={75}^o$, exterior angle $={135}^o$
• C. Base angle $={135}^o$, exterior angle $={45}^o$
• D. Base angle $={67.5}^o$, exterior angle $={75}^o$

Answer 1

The correct option is A Base angle $={67.5}^o$, exterior angle $={135}^o$

Let $x$ be the exterior angle at vertex (in degrees).

Then the exterior angle and the interior angle at vertex form a linear pair.

Then,

$x+{45}^o={180}^o$
$x={180}^o-{45}^o={135}^o$

The $2$ base angles of an isosceles triangle are equal, let us represent each as $z$.

Applying angle sum property,
$z+z+45={180}^o$
$\Rightarrow 2z={180}^o-{45}^o$

$\Rightarrow 2z={135}^o$

$\Rightarrow z={67.5}^o$

So, base angle $={67.5}^o$ , exterior angle $={135}^o$