Question

Triangle ABC is a right triangle.

What is the relationship between angles A and B?

They are congruent.
They are complementary.
They are supplementary.

Answer 1

A and B are complementary angles.

Explanation:

We know that triangle ABC is a right angled triangle so one of the angles among A, B or C is 90°.

The sum of all three angles of a triangle is 180° so assuming angle C to be the right angle (i.e. 90°), we can write it as:

`A+B+C=180`°

`A+B+90= 180`°

`A+B=180-90`

`A+B= 90`

We know that if two angles add up to a sum of 90°, they are said to be complementary angles.

Since here in this case,
`A+B= 90`, therefore A and B are complementary angles.

Answer 2

we are given

Triangle ABC is a right triangle

It means that one of angle is at right angled

Let's assume angle C is at right angled

so,

`C=90`

now, we know that sum of all three angles of any triangle is always 180

so,

`A+B+C=180`

we can plug C=90

`A+B+90=180`

Subtract both sides by 90

`A+B+90-90=180-90`

`A+B=90`

We know that

when sum of two angles are 90 degree or at right angle

then those two angles are complementary angles

so,

They are complementary..........Answer