Advertisements
Advertisements
Question
If an angle of a triangle is equal to the sum of the other two angles, find the type of the triangle
Solution
Let ∠B is the greater angle than by the given condition ∠B = ∠A + ∠C.
Sum of three angles of a triangle = 180°
∠A + ∠B + ∠C = 180°
∠A + (∠A + ∠C) + ∠C = 180°
2∠A + 2∠C = 180°
2(∠A + ∠C) = 180°
∠A + ∠C = `(180^circ)/2`
∠B = 90°
∴ One of the angle of the triangle = 90°
It will be a right angled triangle.
APPEARS IN
RELATED QUESTIONS
The angles of a triangle are (x − 40)°, (x − 20)° and `(1/2x-10)^@.` find the value of x
ABC is a triangle in which ∠A — 72°, the internal bisectors of angles B and C meet in O.
Find the magnitude of ∠BOC.
Is the following statement true and false :
An exterior angle of a triangle is greater than the opposite interior angles.
Mark the correct alternative in each of the following:
If all the three angles of a triangle are equal, then each one of them is equal to
If two acute angles of a right triangle are equal, then each acute is equal to
Find the value of the angle in the given figure:
Find the unknown marked angles in the given figure:
Find, giving a reason, the unknown marked angles, in a triangle drawn below:
The exterior angle of a triangle is equal to the sum of two
Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than `2/3` of a right angle.
