Question

Find, giving reasons, the unknown marked angles in each triangle drawn below:

Answer 1

Finding $x$ by using an exterior angle property of a triangle

We know that,
An exterior angle of a triangle is always equal to the sum of its two opposite interior angles.

Therefore,
$\angle ACD=\angle BAC+\angle ABC$
$\Rightarrow {110}^{\circ }=x+{30}^{\circ }----\left(1\right)$

From equation (1)
we get,
$x^{\circ }={110}^{\circ }-{30}^{\circ }$
$\Rightarrow x^{\circ }={80}^{\circ }$

Hence, the unknown marked angle $x$ is ${80}^{\circ }$