Question

The four angles of a quadrilateral are 2(x - 10.º. (x + 30), (x + 50)° and 2xº. Find all
the four angles.​

Answer 1

Answer:

2x-20+x+30+x+50+2x=360

sum of angles of quadrilateral = 360

6x-60=360

6x=360+60

6x=420

x=420/6=70

2(x-10)= 2*(70-10)=120°

x+30=70+30=100°

x+50=70+50=120°

2*70=140°

The four angles are 120°,100°,120°,140°

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Answer 2

Given :

The four angles of a quadrilateral are 2(x - 10)º, (x + 30)°, (x + 50)° and 2xº.

To Find :

All angles of the quadrilateral.

Solution :

Analysis :

We know that the sum of interior angles of quadrilateral is 360°. Using that information we will find the angles.

Explanation :

We know that all interior angles of a quadrilateral add upto 360°.

• 2(x - 10)°
• (x + 30)°
• (x + 50)°
• 2x°

☯ According to the question,

⇒ 2(x - 10)° + (x + 30)° + (x + 50)° + 2x° = 360°

⇒ (2x - 20)° + (x + 30)° + (x + 50)° + 2x° = 360°

Expanding the brackets,

⇒ 2x - 20 + x + 30 + x + 50 + 2x = 360

Arranging the variables,

⇒ 2x + x + x + 2x - 20 + 30 + 50 = 360

⇒ 6x - 20 + 80 = 360

⇒ 6x + 60 = 360

Transposing 60 to RHS,

⇒ 6x = 360 - 60

⇒ 6x = 300

⇒ x = 300/6

⇒ x = 50

∴ x = 50.

The angles :

1. 2(x - 10)° = 2(50 - 10) = 2(40) = 2 × 40 = 80°
2. (x + 30)° = (50 + 30)° = 80°
3. (x + 50)° = (50 + 50) = 100°
4. 2x° = 2 × 50 = 100°

The angles are 100°, 100°, 80°, 80°.

Verification :

LHS :

⇒ 2(x - 10)° + (x + 30)° + (x + 50)° + 2x°

⇒ 80° + 80° + 100° + 100°

⇒360°

RHS :

360°

∴ LHS = RHS.

• Hence verified.