Question

prove that if one angle of triangle is equal to sum of other two angles, then the triangle is a right angle​

Answer 1

Answer:

Step-by-step explanation:

Let the angles be a,b,c where a = b+c

As we know

a+b+c = 180° ( ASP of triangle)

Since,

a = b+c -------------- 1

Therefore ,

b+c+b+c = 180° ( from 1)

2 ( b+c) = 180°

b + c = 180°/2

b + c = 90°

Putting value of b+c in equation 1

a = b+c

a = 90°

Since ,

a = 90°

Therefore,

Given triangle is right angled

Answer 2

Step-by-step explanation:

1.............

The angles in a triangle add up to 180 degrees. So if your triangle is such that one angle( call it x) is equal to the sum of the two ( a+b) angles then two conditions must be met:

1.x = a+b

2. x+a+b=180

this means 2x=180

thus x = 90 degrees.

so a+b = 90. so a and b can take any values that sum to 90 eg. (42, 48) (60,30) (70,20) etc. In other words a and b are complementary. The triangle is a right-angled triangle

2.............

Let ABC be a triangle.

Let angle B = 90 degree

According to the question,

Angle A + Angle C = 90

A and C should be acute angles.

Some values of A and C are :

A and C

30&60

60&30

45&45

Since one of the angle is 90o90o , so the triangle is a right angle triangle.

In a right angled triangle, the longest side (hypotenuse) is always opposite to 90 degree and the other two angles are acute angles.

I hope this is your required answer.