Question

Find the measures of x and y

Answer 1

m∠x = 159°

m∠y = 140°

Explanation:

PART I: Find the measure of y

Given information

∠a = 40°

Given formula

∠a + ∠y = 180° (Supplementary angles)

Substitute values into the formula

40 + ∠y = 180

∠y = 180 - 40

`\Large\boxed{\angle y=140^\circ}`

PART II: Find the measure of x

Given information

∠b = 61°

∠c = Supplementary angle of ∠b

Given formula

∠b + ∠c = 180°

Substitute values into the formula

61 + ∠c = 180

∠c = 180 - 61

∠c = 119°

Determine the value of ∠x

∠x = ∠a + ∠c (Exterior angle theorem)

∠x = (40) + (119)

`\Large\boxed{\angle x=159^\circ}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

x = 159; y = 140

Explanation:

a = 40

a + y = 180

y = 180 - 40

y = 140

b = 61

b = (180 - x) + a

61 = 180 - x + 40

x = 159