Angle of a triangle is equal to the sum of the other two show that the triangle is a right angle

If one angle of a triangle is equal to the sum of the other two, show that the triangle is a
right triangle.

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

i.e, `∠ B=∠ A+∠C`

Now, in ΔABC

(Sum of all aangles of triangle `180^@`)

`∠ A+∠B+∠ C=180^@`

`∠ B+∠ B=180^@` [∵ ∠ B=∠ A+∠ C]

`2∠ B=180^@`

`∠ B=180^@/2`

`∠ B=90^@`

∴ABC is a right angled a triangle

Concept: Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle

Is there an error in this question or solution?

Question 8 Properties of Triangle Exercise 15.2

Answer:

Given that one angle of a triangle is equal to the sum of the other two

Let the measure of angles be x, y, z

Therefore we can write above statement as x = y + z

x + y + z = 180

Substituting the above value we get x + x = 180

2x = 180

x = 180/2

x = 90

If one angle is 90 degree then the given triangle is a right angled triangle.

Video transcript

hello everybody welcome to leader learning channel my name is rachna chaudhary and we are going to solve this question question is if one angle of the triangle is equal to the sum of other two angles we have to show that the triangle is a right angle triangle so um we have to let first of all all the three angles so let the angles b x y and z now according to question we are given that one of the angle is equal to the sum of other two so we can say that x can be equal to y plus z we have named this as equation one now according to angle some property we know that sum of all the angles in a triangle is always equal to 180 degree so let's put x plus y plus z is equal to 180 now i'm putting x uh y plus z as x because we can see here that y plus z is equal to x so x is here already and at the pace of y plus z i'm putting x here is equal to 180 i have written the reason since equation 1 now 2x is equal to 180 and the value of x is 180 upon 2 that mean 90. so we have the value of x that x is equal to 90 that mean one of the angle is 90 so if one of the angle is 90 we can say that the given triangle is a right angled triangle or right triangle so i hope you understand the method see you in the next video don't forget to like comment and subscribe thank you

Was This helpful?

Text Solution

Solution : Let, 1st angle /_A 2nd angle angle B 3rd angle `/_C /_A + /_B = /_C` -- Given We know that, `/_A + /_B + /_C = 180^@` `/_C + ( /_A + /_B ) = 180^@` `/_C + /_C = 180^@` `2/_C = 180^@` `/_C = 180/2` `/_C = 90^@` `/_C = 90^@`, Therefore the triangle is right angled.

If one angle of a triangle is equal to the sum of the other two,show that the triangle is a right triangle.

Open in App

Suggest Corrections