Question

The angles of a triangle are in A.P. If the greatest angle is three times the smallest angle, find the greatest angle in the triangle.

• A. ${80}^{\circ }$
• B. ${75}^{\circ }$
• C. ${100}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D

${90}^{\circ }$

Let angles in A.P. be a - d, a, and a + d respectively
$\therefore$ $a-d+a+a+d={180}^{\circ }$
[Angle sum property of triangle]
$\Rightarrow 3a={180}^{\circ }\Rightarrow a={60}^{\circ }$
Also, $a+d=3(a-d)\Rightarrow a+d=3a-3d\Rightarrow 4d=2aora=2d\Rightarrow {60}^{\circ }=2d\Rightarrow d={30}^{\circ }$
$\therefore$ Required angles are $(a-d{)}^{\circ },a^{\circ }and(a+d{)}^{\circ }={60}^{\circ }-{30}^{\circ },{60}^{\circ }and{60}^{\circ }+{30}^{\circ }={30}^{\circ },{60}^{\circ }and{90}^{\circ }$