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Sagot :

Answer:

80° , 100°, 80°

Step-by-step explanation:

∠ 1 and ∠ 2 form a straight line and sum to 180° , then

2x + 40 + 2y + 40 = 180

2x + 2y + 80 = 180 ( subtract 80 from both sides )

2x + 2y = 100 → (1)

∠ 1 and ∠ 3 are vertical angles and are congruent , then

2x + 40 = x + 2y ( subtract x from both sides )

x + 40 = 2y ( subtract 40 from both sides )

x = 2y - 40 → (2)

Substitute x = 2y - 40 into (1)

2(2y - 40) + 2y = 100

4y - 80 + 2y = 100

6y - 80 = 100 ( add 80 to both sides )

6y = 180 ( divide both sides by 6 )

y = 30

Substitute y = 30 into (2)

x = 2(30) - 40 = 60 - 40 = 20

Thus x = 20 and y = 30

Then

∠ 1 = 2x + 40 = 2(20) + 40 = 40 + 40 = 80°

∠ 2 = 2y + 40 = 2(30) + 40 = 60 + 40 = 100°

∠3 = x + 2y = 20 + 2(30) = 20 + 60 = 80°

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