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Geometry — MATHS STD 6 — Question

Gujarat BoardEnglish MediumSTD 6MATHSGeometry3 Marks
Question
Can we have two acute angles whose sum is:
$a.\ $An acute angle? Why or why not?
$b.\ $A right angle? Why or why not?
$c.\ $An obtuse angle? Why or why not?
$d.\ $A straight angle? Why or why not?
$e.\ $A reflex angle? Why or why not?
✓

Answer

$a.\ $Yes, the sum of the two acute angles may be less than a right angle, e.g. $30^\circ $ and $45^\circ $ are acute angles and their sum (i.e. $30^\circ + 45^\circ = 75^\circ $) is also an acute angle.
$b.\ $Yes, the sum of two acute angles may be equal to a right angle, e.g. $30^\circ + 60^\circ = 90^\circ .$
$c.\ $Yes, the sum of two acute angles may be more than a right angle, i.e. obtuse angle, e.g. $60^\circ + 70^\circ = 130^\circ .$
$d.\ $No, the sum of two acute angles is always less than a straight angle, i.e. $180^\circ .$
$e.\ $No, the sum of two acute angles is always less than $180^\circ $. So, their sum cannot be a reflex angle.

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