Question

18. Two angle of a triangle are equal and third angle is greater than each one of them by 18°. Find the angles.
19. If the base of isosceles triangl is produced on both sides prove that the exterior angle so formed are equal to​

Answer 1

Step-by-step explanation:

1.Let each equal be x, and other angle be (x + 18)°

We know, sum of all angles of a triangle = 180°

x + x + (x + 18) = 180

x + x + x + 18 = 180

3x = 180 - 18

3x = 162

x = 162/3

x = 54°

Angles are :

x = 54°

x = 54°

x + 18 = 54 + 18 = 72°

Answer 2

$\huge\red{Ⓐⓝⓢⓦⓔⓡ}$

18.

Consider ∠A and ∠B in a triangle is x°

We know that the sum of all the angles in a triangle is 180°.

So we can write it as

∠A + ∠B + ∠C = 180°

By substituting the values

x°+ x° + ∠C = 180°

By addition

2x°+ ∠C = 180°….. (1)

According to the question we get

∠C = x° + 18°……. (2)

By substituting (2) in (1) we get

2x°+ x° + 18° = 180°

On further calculation

3x° + 18° = 180°

By subtraction

3x°= 180°– 18°

3x°= 162°

By division

x°= 162/3

x° = 54°

By substituting the values of x

∠A = ∠B = 54°

∠C = 54°+ 18°= 72°

Therefore, ∠A = 54°, ∠B = 54° and ∠C = 72°

19.

ED is a straight line segment and B and C are points on it.

⇒∠EBC=∠BCD=straight∠=180∘

⇒∠EBA+∠ABC = ∠ACB +∠ACD

⇒∠EBA = ∠ACD +=ACB -∠ABC

⇒∠EBA=∠ACD [From (1) ∠ABC =∠ACD]

⇒∠ABE = ∠ACD

∴Hence proved

FOLLOW ME ♥️