Question

Which of the following angles can form a triangle ?

• A. ${60}^{\circ },{105}^{\circ },{120}^{\circ }$
• B. ${45}^{\circ },{85}^{\circ },{60}^{\circ }$
• C. ${95}^{\circ },{15}^{\circ },{80}^{\circ }$
• D. ${65}^{\circ },{105}^{\circ },{10}^{\circ }$

Answer 1

The correct option is D

${65}^{\circ },{105}^{\circ },{10}^{\circ }$

The sum of angles in a triangle is ${180}^{\circ }.$

${60}^{\circ }+{105}^{\circ }+{120}^{\circ }={285}^{\circ }>{180}^{\circ }$
${45}^{\circ }+{85}^{\circ }+{60}^{\circ }={190}^{\circ }>{180}^{\circ }$
${95}^{\circ }+{15}^{\circ }+{80}^{\circ }={190}^{\circ }>{180}^{\circ }$

But,
${65}^{\circ }+{105}^{\circ }+{10}^{\circ }={180}^{\circ }.$
Thus, the angles ${65}^{\circ },{105}^{\circ }$ and ${10}^{\circ }$ can form a triangle.