Question

Please help? Angle Sum theorem. Find z,x,y and w

Answer 1

sum of angles in a triangle is 180 sox + 42 +73 = 180
we can find angle x in triangle x = 65

y + 131 = 180 ( adjacent supplementary angles ) y = 49

we can find now the the third angle of the triangle x + y + this angle = 180
65+ 49 + this angle = 180
so this angle = 66
this angle is adjacent supplementary with angle z
this angle + z = 180
66+ z = 180
z = 114

Answer 2

x = 65°

y = 49°

z = 114°

w = 93°

Explanation:

Since ∠y + 131° = 180°

So ∠y = 180° - 131°

= 49°

From ΔDEF,

∠x + 42° + 73° = 180°

∠x + 115° = 180°

∠x = 180 - 115

= 65°

From ΔDGL

∠x + ∠y + ∠DLG = 180°

65° + 49° + ∠DLG = 180°

∠DLG = 180 - 114

= 66°

Now ∠z + ∠DLG = 180° [Supplementary angles]

∠z = 180 - 66

= 114°

From ΔIJC,

∠142° + ∠IJC = 180° [ Supplementary angles]

∠IJC = 180 - 142

= 38°

w + 38° + 49°=180°

w + 87° = 180°

w = 180° - 87°

w = 93°