Answer:
1. C = 360 - (77 + 123 + 86) = 74
2. x = 252
D = 290
3. x = 20
S = 47
P = 131
4. 36, 72, 108, 144
Step-by-step explanation:
Quadrilaterals are composed of two triangles. Seeing as we know the sum of the interior angles of a triangle is 180°, it follows that the sum of the interior angles of a quadrilateral is 360°.
1. C = 360 - (77 + 123 + 86) = 74
2. x + 38 = 360 - (124 + 97 + 69) = 290
x = 290 - 38 = 252
D = 290
3. (27 + x) + (3x + 71) = 360 - (119 + 63)
27 + x + 3x + 71 = 178
4x = 80
x = 20
S = 27 + x = 27 + 20 = 47
P = 3x + 71 = 3(20) + 71 = 131
4. Let angles be x, 2x, 3x, 4x then
x + 2x + 3x + 4x = 360
10x = 360
x = 36
then the angles are 36, 72, 108, 144
