Question

In a triangle 𝐴𝐵𝐶, ∠𝐴=${45}^{\circ }$ and ∠𝐵=${75}^{\circ }$. Find ∠𝐶.

Answer 1

Step: Find ∠C

Given: ∠A=${45}^{\circ }$ and ∠B=${75}^{\circ }$.

We know that sum of angles of a triangle = ${180}^{\circ }$.

⇒ ∠A+∠B+∠C = ${180}^{\circ }$.

⇒ ${45}^{\circ }$+${75}^{\circ }$+∠C = ${180}^{\circ }$.

⇒ ${120}^{\circ }$+∠C =${180}^{\circ }$.

⇒ ∠C = ${180}^{\circ }$ -${120}^{\circ }$.

⇒ ∠C = ${60}^{\circ }$.

Hence, the value of ∠C is ${60}^{\circ }$.