Question

What of the following is correct ?

• A. $\angle DEF={137}^o$ is an obtuse angle.
• B. $\angle DEF={127}^o$ is an obtuse angle
• C. $\angle DEC={37}^o$ is an obtuse angle
• D. $\angle DEG={53}^o$ is an obtuse angle.

Answer 1

The correct option is B $\angle DEF={127}^o$ is an obtuse angle

In the given figure,
We know, if two rays having common vertex make straight line then angle between both rays will be ${180}^o$
$\angle CEF+\angle DEC+\angle DEG={180}^o\Rightarrow {90}^o+\angle DEC+{53}^o={180}^o\Rightarrow \angle DEC={180}^o-({90}^o+{53}^o)\Rightarrow \angle DEC={180}^o-{143}^o\Rightarrow \angle DEC={37}^o$

Hence, $\angle DEF=\angle DEC+\angle CEF={37}^o+{90}^o={127}^o$
$\angle DEF$ is an obtuse angle because it is greater than ${90}^o$ and less than ${180}^o$