Question

What are the measures of ∠CED and ∠BCE in the figure?

Answer 1

∠CED = 70°

∠BCE = 134°

Explanation:

Finding z :

• ∠EDC = ∠ABC (Alternate angles)
• 8z = 64
• z = 8

Finding ∠CED :

• ∠CED = 9z - 2
• ∠CED = 9(8) - 2
• ∠CED = 70°

Finding y :

• ∠CDE = ∠BAC (Alternate angles)
• 70 = 3y + 10
• 3y = 60
• y = 20

Finding ∠BCE :

• ∠BCE = 7y- 6
• ∠BCE = 7(20) - 6
• ∠BCE = 134°

Answer 2

∠CED = 70°

∠BCE = 134°

Explanation:

We don't know if AB and DE are parallel (since there are no arrows on these line segments), therefore we cannot use the Alternate Interior Angles Theorem at this point to definitively say that ∠CDE = ∠ABC.

Angles around a point sum to 360°

Angles on a straight line sum to 180°

⇒ ∠ACB + ∠BCE = 180

⇒ ∠ACB + (7y - 6) = 180

⇒ ∠ACB = 180 - (7y - 6)

⇒ ∠ACB = 180 - 7y + 6

⇒ ∠ACB = 180 - 7y + 6

⇒ ∠ACB = 186 - 7y

The interior angles of a triangle sum to 180°

⇒ ∠ACB + ∠CBA + ∠BAC= 180

⇒ 186 - 7y + 64 + 3y + 10 = 180

⇒ 260 - 4y = 180

⇒ 4y = 80

⇒ y = 20

Using the found value of y to find ∠BCE:

⇒ ∠BCE = 7(20) - 6

⇒ ∠BCE = 134°

Angles on a straight line sum to 180°

⇒ ∠DCE + ∠BCE = 180

⇒ ∠DCE + 134 = 180

⇒ ∠DCE = 46°

The interior angles of a triangle sum to 180°

⇒ ∠DCE + ∠CED+ ∠EDC = 180

⇒ 46 + (9z - 2) + 8z = 180

⇒ 17z + 44 = 180

⇒ 17z = 136

⇒ z = 8

Using the found value of z to find ∠CED:

⇒ ∠CED = 9(8) - 2

⇒ ∠CED = 70°