If one angle of a triangle is equal to the sum of the other two angles

1.	If one angle of a triangle is equal to the sum of the other two angles, then the triangle is(A) An isosceles triangle(B) An obtuse triangle(C) An equilateral triangle(D) A right triangle
Answer» (D) A right triangle Explanation: Let the angles of △ABC be ∠A, ∠B and ∠C Given that ∠A= ∠B+∠C …(eq1) But, in any △ABC, Using angle sum property, we have, ∠A+∠B+∠C=180^o …(eq2) From equations (eq1) and (eq2), we get ∠A+∠A=180^o ⇒2∠A=180^o ⇒∠A=180^o/2 = 90^o ⇒∠A = 90^o Hence, we get that the triangle is a right triangle Therefore, option (D) is the correct answer.

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is(A) An isosceles triangle(B) An obtuse triangle(C) An equilateral triangle(D) A right triangle

Answer»

(D) A right triangle

Explanation:

Let the angles of △ABC be ∠A, ∠B and ∠C

Given that ∠A= ∠B+∠C …(eq1)

But, in any △ABC,

Using angle sum property, we have,

∠A+∠B+∠C=180^o …(eq2)

From equations (eq1) and (eq2), we get

∠A+∠A=180^o

⇒2∠A=180^o

⇒∠A=180^o/2 = 90^o

⇒∠A = 90^o

Hence, we get that the triangle is a right triangle

Therefore, option (D) is the correct answer.