Question

Find the value of $\angle CAB+\angle CBA$ from the following figure.

• A. ${130}^{\circ }$
• B. ${50}^{\circ }$
• C. ${80}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is A ${130}^{\circ }$

Consider $\Delta ADC$,
$\angle D={180}^{\circ }-({80}^{\circ }+{50}^{\circ })={50}^{\circ }$ $(\because$ angle sum property of triangle)

$\angle D=\angle C$ (By converse of the theorem , if a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle)

$\angle C={50}^{\circ }$

$\angle CAB+\angle CBA$ = ${180}^{\circ }-\angle C$
= 130${}^{\circ }$