Lines and Angles Test - 5

we know that exterior angle so formed is equal to the sum of the two interior opposite angles

 Let the two interior opposite angles be x

so

x + x = 80⁰

2x = 80⁰

x = 40⁰

 We know that two angles, whose sum is 90°, are called complimentary angle

let one angle be x then its complimentary angle be 8x

x + 8x = 90⁰

9x = 90⁰

x = 10⁰

its complimentary angle is 8x10 = 80⁰

Let the angles of the triange be 5x,3x and 7x

We know that the sum of the angles of a triangle is 180º

5x + 3x + 7x = 180º

15x = 180º

x = 12⁰

Therefore the angles are

5x = 5 × 12⁰ = 60⁰

3x = 3 × 12⁰ = 36⁰

7x = 7 × 12⁰ = 4⁰

Since all the angles are less than 90⁰ there fore it is a acute angled triangle.

The sum of the angles of triangle  is 180 degrees.
let the angles of triangle be a ,  b, c

we have given that one angle of a triangle is equal to the sum of the other two angles

so we have
c=a + b
a + b + c = 180
Substitute c for a +b

c + c = 180
2c = 180
c = 90

therefore the triangle is a right triangle.

Two angles, whose sum is 90°, are called complimentary angle

let x is a complimentary angle of (9000 – a)

x + (9000 – a) = 90⁰

x = 90⁰- (9000 – a)

x = 90⁰- 9000 + a

x = a⁰