Question

1. Solve: 9a + 5 = 68
2. Two angles of a triangle are 30° and 80°.Find the third angle.
3. Determine whether the triangle whose lengths of sides are 3cm,4cm, 5cm is a right-angled triangle.

Answer 1

Answer:

1) a = 63/9

2) 30° + 80°+x° = 180°

x° = 90

3) Yes it is.

Answer 2

1. 9a + 5 = 68

--> 9a = 68 - 5

--> a = 63/9

--> a = 7

∴ Value of X = 7

2. Given: 2 angles 30⁰ & 80⁰.

To find: 3rd angle

Let the 3rd angle be "x"

By Angle Sum Property we know that, sum of all the angles in a triangle is 180⁰.

I.e, 30⁰ + 80⁰ + x = 180⁰

--> x = 180⁰ - 80⁰ - 30⁰

--> x = 70⁰

∴ The third angle is 70⁰

3. To know whether a triangle is right-angled, we must know about the pythogorean theorem.

I.e, in a right triangle, altitude² + base² = hypotenuse²

GIVEN: Lengths of sides 3cm, 4cm, 5cm

So, we have to prove that 3² + 4² = 5²

Take LHS, 3² + 4²

--> 9 + 16

--> 25

Take RHS, 5²

--> 25

LHS = RHS = 25

∴ 3² + 4² = 5²

∴ The triangle is right angled