Question

In the given figure , AE is the diameter of the circle. Write down the numerical value of $\angle ABC+\angle CDE$.

• A. ${360}^{\circ }$
• B. ${540}^{\circ }$
• C. ${180}^{\circ }$
• D. ${270}^{\circ }$

Answer 1

Answer: (D)

${270}^{\circ }$

Join AD

In the cyclic quadrilateral ABCD

$\angle ABC+\angle ADC={180}^{\circ }$........(i)(opp.$\angle s$ angle of a cyclic quadrilateral are supplementary)

Also $\angle ADE={90}^{\circ }$ .....(ii)(Angle in a semicircle is a right angle)

$\therefore$ Adding eqns (i) and (ii), we get

$\angle ABC+\angle ADC+\angle ADE={180}^{\circ }+{90}^{\circ }$

$\Rightarrow \angle ABC+\angle CDE={270}^{\circ }$