Question

In which of the following cases, the measure of three angles are given. State which of the groups from a triangle:

• A. ${65}^o,{35}^o,{80}^o$
• B. ${45}^o,{45}^o,{60}^o$
• C. ${48}^o,{43}^o,{83}^o$
• D. ${20}^o,{100}^o,{80}^o$

Answer 1

Answer: (A)

We know that, Angle sum property of triangle is,

Sum of all the angles of a triangle $={180}^{\circ }$

Now, we will check the options,

A. ${65}^{\circ },{35}^{\circ },{80}^{\circ }$

${65}^{\circ }+{35}^{\circ }+{80}^{\circ }={180}^{\circ }$

$\therefore$ ${65}^{\circ },{35}^{\circ },{80}^{\circ }$ are the $3$ angles of a triangle

B. ${45}^{\circ },{45}^{\circ },{60}^{\circ }$

${45}^{\circ }+{45}^{\circ }+{60}^{\circ }={150}^{\circ }\ne {180}^{\circ }$

So, these are not angles of triangle.

C. ${48}^{\circ },{43}^{\circ },{83}^{\circ }$

${48}^{\circ }+{43}^{\circ }+{83}^{\circ }={174}^{\circ }\ne {180}^{\circ }$

So, these are not angles of triangle.

D. ${20}^{\circ },{100}^{\circ },{80}^{\circ }$

${20}^{\circ }+{100}^{\circ }+{80}^{\circ }={200}^{\circ }\ne {180}^{\circ }$

So, these are not angles of triangle.

Hence, Option A is correct.