Question

Sum of two angles of a quadrilateral in the ratio 1:3 is 200°. If the other two angles of the quadrilateral are equal , find all four angles of the quadrilateral. Also, find the measure of all the exterior angles​

Answer 1

Answer:

Let the angles be x and 3x

According to question:-

x+3x=200

4x=200

$x = \frac{200}{4}$

x=50°

1st angle=x

=50°

2nd angle=3x

=3(50°)

=150°

Let the other angles be y

200°+y+y=360°

200°+2y=360°

2y=360°-200°

2y=160°

$y = \frac{160}{2}$

y=80°

All interior angles:-

1st angle=50°

2nd angle=150°

3rd angle=80°

4th angle=80°

All exterior angles:-

Property:-

Interior angle+Exterior angle=180°

1st angle:-

50+Exterior angle=180°

Exterior angle=180°-50°

=130°

2nd angle:-

150°+Exterior angle=180°

Exterior angle=180°-150°

=30°

3rd angle:-

80°+Exterior angle=180°

Exterior angle=180°-80°

=100°

4th angle:-

80°+Exterior angle=180°

Exterior angle=180°-80°

=100°