a. The value of x for the interior angles of the quadrilateral is 20.
b. The value of x for the exterior angles of the triangle is 39.
The sum of the interior angles of a four sided polygon also called a quadrilateral is equal to 360° so for the given quadrilateral, the value of x is calculated as:
5x + 20 + 4x + 5x - 10 + 3x + 10 = 360°
17x + 20 = 360°
17x = 360 - 20 {collect like terms}
17x = 340
x = 340/17 {divide through by 17}
x = 20.
The sum of the exterior angles of a triangle is equal to 360°, thus;
2x + 3x + 15 + 150 = 360°
5x + 165 = 360°
5x = 360 - 165 {collect like terms}
5x = 195
x = 195/5 {divide through by 5}
x = 39.
Therefore, the value of x for the interior angles of the quadrilateral and the exterior angles of the triangle are 20 and 39 respectively.