Question

find x and y in the figure​

Answer 1

Answer:

x = 80° and y = 75°

Step-by-step explanation:

• First Let's Solve For x

⇒ 30° + 50° = x   (Exterior Angle Property)

⇒ x = 80°

• Now Solve for y

⇒ x + 45° + ∠CAD = 180°     (Angle Sum Property)

⇒ 80° + 45° + ∠CAD = 180°

⇒ 125° + ∠CAD = 180°

⇒ 125° + ∠CAD - 125° = 180° - 125°

⇒ ∠CAD = 55°

50° + ∠CAD + y = 180° (Straight Line Angle Property)

⇒ 50° + 55° + y = 180°

⇒ 105° + y = 180°

⇒ 105° + y - 105° = 180° - 105°

⇒ y = 75°

Answer 2

★$\large\mathfrak \pink{Solution:-}$

★$\underline \mathbb{GIVEN:-}$

☯∠ABC = 30°

☯∠BAC = 50°

☯∠ADC = 45°

★$\underline \mathbb{TO \: FIND:-}$

☯∠ACD (x)

☯∠DAE (y)

★$\underline \mathbb{FORMULA:-}$

1)Sum of all the 3 angles of a triangle is 180°

2)The sum of linear pair is 180°

★$\underline \mathbb{BY \: THE \: PROBLEM:-}$

☯∠ABC + ∠BAC + ∠ACB = 180° (By Formula 1)

or, 30° + 50° + ∠ACB = 180°

or, 80° + ∠ACB = 180°

or, ∠ACB = 180° - 80°

or, ∠ACB = 100°

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☯∠ACB + ∠ACD = 180° (By Formula 2)

or, 100° + ∠ACD = 180°

or, ∠ACD = 180° - 100°

or, ∠ACD (x) = 80°

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☯∠ADC + ∠ACD + ∠CAD = 180° (By Formula 1)

or, 45° + 80° + ∠CAD = 180°

or, 125° + ∠CAD = 180°

or, ∠CAD = 180° - 125°

or, CAD = 55°

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☯∠BAC + ∠CAD + ∠DAE = 180° (By Formula 2)

or, 50° + 55° + ∠DAE = 180°

or, 105° + ∠DAE = 180°

or, ∠DAE = 180° - 105°

or, ∠DAE (y) = 75°

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★$\underline \mathbb{ANSWER:-}$

☯∠ACD (x) = 80°

☯∠DAE (y) = 75°