Prove that if one angle of a triangle is 90°, then the other two add to 90°.
A right-angled triangle has one angle equal to 90º and the other two angles are acute angles.
Answer: Hence proved that the sum of the other two angles of a right-angled triangle is 90°.
Let's prove.
Explanation:
Given: In the above triangle ABC, ∠B = 90º
∠A and ∠C are acute angles. Let ∠A be x and ∠B be y.
By angle sum property of triangles,
⇒ ∠A + ∠B + ∠C = 180º
⇒ x + y + 90º = 180º
⇒ x + y = 180º - 90º
⇒ x + y = 90º
Hence proved.