Question

Given: $\angle CAB={75}^o$ and $\angle CBA={50}^o$. Find the value of $\angle DAB+\angle ABD$.

Answer 1

$In\Delta ABC$

$\angle ABC=\angle ACB=\angle BAC={180}^0$ (by angle sum of property)

${50}^0+\angle ACB+{75}^0={180}^0$

$\angle ACB+{125}^0={180}^0$

$\angle ACB={180}^0-{125}^0$

$\angle ACB={55}^0$

$\angle ADB=\angle ACB={55}^0$ ( angle subtended by an arc in the same segment are equal)

$Now$

$In\Delta ABD$

$\angle ADB+\angle DAB+\angle ABD={180}^0$ ( by angle sum property)

${55}^0+\angle DAB+\angle ABD={180}^0$

$\angle DAB+\angle ABD={180}^0-{55}^0$

$\angle DAB+\angle ABD={125}^0$