Question

In the figure,two of the angles are indicated. What are the measures of $\angle ACXand\angle ACB?$

Answer 1

Given that in $\Delta ABC,\angle A={50}^{\circ }and\angle B={55}^{\circ }$
We know that the sum of angles in a triangle is ${180}^{\circ }$
Therefore we have
$\angle A+\angle B+\angle C={180}^{\circ }$
${50}^{\circ }+{55}^{\circ }+\angle C={180}^{\circ }$
$\angle C={75}^{\circ }$
$\angle ACB={75}^{\circ }$
$\angle ACX={180}^{\circ }-\angle ACB={180}^{\circ }-{75}^{\circ }={105}^{\circ }$