Question

the four angle of a quadrilateral are 2(x-10)°, (x+30)°, (x+50)° and 2x°. find all the four angles.​

Answer 1

Step-by-step explanation:

Sum of angles of Quadrilateral ia 360°

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

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

6x - 20 + 30 + 50 = 360

6x + 60 = 360

6x = 300

x = 50°

FOUR ANGLE ARE :-

• 2(x-10)° = 2 * 40 = 80°
• (x+30)° = 50 + 30 = 80°
• (x+50)° = 50 + 50 = 100°
• 2x° = 2 * 50 = 100°

Answer 2

Aim:-

With the four given angles of a quadrilateral $2(x-10), (x+30),(x+50)$ and $2x$,  we need to find the angles of the quadrilateral.

Procedure of solving:-

• The given values are added.
• The sum is equated to 360° as it is the sum of all four angles of any quadrilateral.
• By using the method of transposing, we can find the value of $x$.
• Substituting the value of $x$, the values of the angles of the quadrilateral can be found.

Solution:-

By Angle Sum Property of a quadrilateral,

$2(x-10)+(x+30)+(x+50)+2x=360$

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

$6x+60=360$

$6x=360-60$

$6x=300$

$x=\frac{300}{6}$

$\boxed{x=50}$

Substituting the value of $x$,

$2(x-10)=2(50-10)\\2(x-10)=2\times40\\\boxed{2(x-10)=80}$

$(x+30)=50+30\\\boxed{(x+30)=80}$

$(x+50)=50+50\\\boxed{(x+50)=100}$

$2x=2\times50\\\boxed{2x=100}$

∴ The four angles of the quadrilateral are 80°, 80°, 100° and 100°.