Question

Two angles of a quadrilateral are 50° and 70° and other two angles are in the ratio 13:11,then find measures of the remaining two angles.

Answer 1

Let take the other two angles as 13x and 11x.

As we know that the sum of a quadilateral is 360°.
Therefore, 50°+70°+13x+11x=360°
=》120°+24x=360°
=》24x =360°-120°
=》24x =240°
=》x =240÷24
=》x =10

Now, 13x=13×10=130°
11x =11×10=110°

Answer 2

The measure of angle 3 is 130° and that of angle 4 is 110°.

Given: Two angles of a quadrilateral are 50° and 70°

The remaining two angles are in the ratio 13:11

To Find: Measure of the remaining two angles of the quadrilateral

Solution:

We know by the Angle Sum Property,

The Sum of all four angles of a quadrilateral is 360°

Let angle 1 = 50°

Let angle 2 = 70°

Since angle3 : angle4 = 13:11

Let angle 3 = 13x

Let angle 4 = 11x

Angle1 + Angle2 + Angle3 + Angle4 = 360°

50° + 70° + 13x + 11x = 360

24x = 360° - 120°

24x = 240°

x = 10°

By placing the value of x

Angle 3 = 13 x 10

             = 130°

Angle 4 = 11 x 10

             = 110°

Therefore, the measure of angle 3 is 130° and that of angle 4 is 110°.