2023-II-18 – Solving Master

Ans: A

Denote the vertex by $A$ , $B$ , $C$ , $D$ and $E$ as shown in the figure.

I must be true. Add a point $F$ such that $E D // A F // B C$ .

Hence, we have $∠ E A F = b$ and $∠ B A F = a$ . Therefore, $a + b = 90^{\circ}$ .

II must be true. Since $B C // E D$ , $c + d = 180^{\circ}$ .

III may not be true. If $c = 30^{\circ}$ , then by II, $d = 150^{\circ}$ . Hence, we have

$\begin{array}{cl} a + b + c \\ = & 90^{\circ} + 30^{\circ} \\ = & 120^{\circ} \\ \neq & d \end{array}$