Question

find the measurement of the unknown angles in each of the following​

Answer 1

Answer:

x=115° , y=65° , z=115°

b = 72°

Step-by-step explanation:

In the first question,

Given :

∠AOD= 65°

To find:

X,Y and Z.

∠AOD= 65°

CD is a straight line,therefore ∠COD = 180°. [Straight angle property]

∠COD = ∠COA + ∠AOD = z + 65°

180° = z + 65°

z = 180-65 = 115°

Similarly,AB is a straight line and ∠BOA = 180°

∠BOA = ∠BOC + ∠COA = y+z = y + 115

180 = y + 115

y= 180-115=65°

And x+y = 180° since CD is also a straight line.

x= 180-65 = 115°

x=115° , y=65° , z=115°

In the second question,

AE is a straight line therefore angle AOE is 180°

∠AOB + ∠BOC + ∠COD + ∠DOE = ∠AOE

45° + 39° + b + 24° = 180°

b = 180 - 108 = 72°

b=72°

I hope it helps!