Question

The measure of an obtuse angle is added with the measure of another angle $b.$ For what type of angle b, the resulting angle is always a reflex angle?

• A. Acute angle
• B. Obtuse angle
• C. Reflex angle

Answer 1

The correct option is B Obtuse angle

Concept: An angle whose measure is greater than ${180}^o$ and less than ${360}^o$ is know as reflex angle.

Let's take an example.
Acute angle: ${20}^o$
Obtuse angle: ${120}^o$
${20}^o+{120}^o={140}^o$

${140}^o$ is an obtuse angle but not a reflex angle.
$\therefore$ When the measures of an acute angle and an obtuse angle are added, they will not necessarily form a reflex angle.

Let's take another example.
${179}^o$ and ${178}^o$ are two obtuse angles.
${179}^o+{178}^o={357}^o{91}^o+{91}^o={182}^o$

${357}^o\&{182}^o$ are reflex angles.
$\therefore$ When the measures of two obtuse angles are added, a reflex angle is formed.

Similarly, if one angle is a reflex angle and the other is an obtuse angle, then the resulting angle is not necessarily a reflex angle.
${270}^o+{95}^o={365}^o$
We know that ${365}^o$ is not a reflex angle.