Question

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

Answer 1

Answer:

i hope this help you

Step-by-step explanation:

Let ABC be any triangle

In which measure of angleB is equal to the measure of remaining angles that is angleA and angleC

So, in triangle ABC,

angleA + angleC= angleB …………(1)

Now, in triangle

angle A +angle B+ angle C =180°

= angle B + ( angleA + angleC) =180°

= angleB + angleB =180°…………..from(1)

=2 angleB = 180°

= angle B = 180°/2

=angleB= 90°

So, one angle of triangleABC is 90° or if one angle of triangle is 90° this triangle is known as right angled triangle.

So, it is right angled triangle

Answer 2

as if one angle = x

other angles = y , y

by the given clues

x = 2y ............ (1)

x + y + y = 180

x + 2y = 180 ...........(2)

by 1 and 2 equations

2y + 2y = 180

4y = 180

y = $\large\frac{180}{4}$

y = 45

x = 90

hence it is right angle triangle......