Question

Select the statements that are true.

• A. $\angle CDB={49}^{\circ }$
• B. $\angle ABC={43}^{\circ }$
• C. $\angle ACB={88}^{\circ }$
• D. $\angle ACB={28}^{\circ }$

Answer 1

Answer: (A), (B), (C)

The correct options are
A

$\angle CDB={49}^{\circ }$

B

$\angle ABC={43}^{\circ }$

C

$\angle ACB={88}^{\circ }$

$\angle CDB=\angle BAC$ (Angles is the same segment) = ${49}^{\circ }$

$\angle ABC=\angle ADC$ (Angles in the same segment) = ${43}^{\circ }$

$\therefore \angle ADB=\angle ADC+\angle BDC={43}^{\circ }+{49}^{\circ }={92}^{\circ }$ and $\angle ADB+\angle ACB={180}^{\circ }$

(opposite angles of a cyclic quad)

$\therefore \angle ACB={180}^{\circ }-\angle ADB$

$={180}^{\circ }-{92}^{\circ }={88}^{\circ }$