Question

In Fig 10.7 if $\angle DAB={60}^{\circ },\angle ABD={50}^{\circ }$ then $\angle ACB$ is equal to

• A. ${60}^{\circ }$
• B. ${50}^{\circ }$
• C. ${70}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$

In $△ADC,$ we have

$\angle DAC={60}^0$ and $\angle ABD={50}^0$

By angle sum property, in $△ABD$

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

$=>{60}^{\circ }+{50}^{\circ }+\angle ADB={180}^{\circ }$

$=>\angle ADB={180}^{\circ }-{110}^{\circ }$

$=>\angle ADB={70}^{\circ }$

We know that the angles subtended at the circumference by the same arc are equal.

$\therefore \angle ADB=\angle ACB$

$=>\angle ACB={70}^0$