Question

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

Answer 1

Answer:

<A & <B = 80°

<C & <D = 100°

Step-by-step explanation:

<A = 2(x-10)° = 2x-20° --------(1)

<B = x+30°-----------(2)

<C = x+50°-----------(3)

<D = 2x°------------(4)

But we know by angle sum property that,

sum of the angles of a quadrilateral = 360°

ie, <A+<B+<C+<D=360°

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

now add like terms

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

6x+60=360

6x = 360-60

6x = 300

x=300/6

x=50

Substitute value of x in (1), (2), (3) & (4)

<A = 2(50)-20 = 100-20 = 80°

<B = 50+30 = 80°

<C = 50+50 = 100°

<B = 2(50) = 100°