Question

If the angles of a quadrilateral are x°,(x + 20)°,2x°,(3x – 80)°,the the greatest

angle is​

Answer 1

Answer:

Step-by-step explanation:

Angles of quadrilateral =  x°, (x + 20)°, 2x°, (3x – 80)°

=>  x + (x + 20) + 2x +(3x – 80) = 360° (Angle Sum Property of a Quadrilateral)

     7x - 60 = 360

     7x = 360 + 60

     7x = 420

       x = $\frac{420}{7}$

       x = 60

∴ The angles are  x° = 60°

                             (x + 20)° = 60 + 20 =80°

                             2x° = 2(60) = 120°

                             (3x – 80)° = 3(60) - 80 = 180 -80 = 100°

∴The greatest angle in the quadrilateral = 2x° = 120°

Answer 2

Answer:

$\bf \fbox \red { The value of x is 60⁰ }$

Step-by-step explanation:

Angles are = x⁰ , ( x + 20⁰ ) , 2x⁰ , ( 3x - 80 )⁰

We know that, the

Sum of all the angles of a quadrilateral = 360⁰

Therefore;

$x⁰ + ( x + 20⁰ ) + 2x⁰ + ( 3x - 80 )⁰ = {360}^{0} \\ \\ x + x + 20 + 2x + 3x - 80 = 360 \\ \\ 7x - 60 = 360 \\ \\ 7x = 360 + 60 \\ \\ x = \frac{420}{7} \\ \\ x = 60 \:$

$\bf \fbox \green {Hence the value of x is 60⁰ }$