Question

In the figure above, which of the following is greatest?

• A. $a$
• B. $b$
• C. $c$
• D. $d$
• E. $e$

Answer 1

The correct option is D $d$

In the given figure,

Sum of angles of a triangle $=$ $180$

$c$ $+$ $60$ $+$ $70$ $=$ $180$

$c$ $+$ $130$ $=$ $180$

$c$ $=$ $180$ $-$ $130$

$c$ $=$ $50$

Sum of angles in a straight line $=$ $180$

$c$ $+$ $d$ $=$ $180$

$50$ $+$ $d$ $=$ $180$

$d$ $=$ $180$ $-$ $50$

$d$ $=$ $130$

An Exterior angle is equal to the sum of the two opposite interior angles of a triangle.

$e$ $=$ $c$ $+$ $60$

$e$ $=$ $50$ $+$ $60$

$e$ $=$ $110$

$b$ $=$ $c$ $+$ $70$

$b$ $=$ $50$ $+$ $70$

$b$ $=$ $120$

Vertically opposite angles across the two lines are equal $a$ $=$ $60$

Here, $a$ $=$ $60$, $b$ $=$ $120$, $c$ $=$ $50$, $d$ $=$ $130$, $e$ $=$ $110$

$d$ $>$ $b$ $>$ $e$ $>$ $a$ $>$ $c$

Therefore, ${}^{\prime }{d}^{\prime }$ is the greatest.