Question

Pls answer these questions with steps
1) in a quadrilateral, sum of three angles is equal to twice the 4th angle. Find the measure of 4th angle.

2) in a quadrilateral shown, the 2 exterior angles are 100° & 120°. If the other two angles are equal, what is the measure of each.

Answer 1

Let a, b, c, d be d the four angles of quadrilateral
Now sum of first three angles is equal to twice the fourth angle
So a+b+c=2d...........( 1note )
Sum of measure of angles of quadrilateral is 360°
Thus, a+b+c+d=360°...........(note 2)
2d+d=360°........ From 1&2
3d=360°
d=120°
Thus measure of fourth angle of quadrilateral is 120°

Answer 2

Let a, b, c, d be d the four angles of quadrilateral 
Now sum of first three angles is equal to twice the fourth angle
So a+b+c=2d...........( 1note )
Sum of measure of angles of quadrilateral is 360°
Thus, a+b+c+d=360°...........(note 2)
2d+d=360°........ From 1&2
3d=360°
d=120° 
Thus measure of fourth angle of quadrilateral is 120°