Question

Use the Exterior Angle Theorem to find the measure of each angle.

mangleC =
mangleD =
mangleDEC =

Answer 1

∠C = 35°

∠D = 76°

∠DEC = 69°

Explanation:

Exterior angle theorem:

Exterior angle equals the sum of opposite interior angles (remote angles).

∠C + ∠D = ∠DEF

3y + 5 + 7y + 6 = 111°

3y + 7y + 5 + 6 = 111

Combine like terms,

10y + 11 = 111

Subtract 11 from both sides,

10y = 111 - 11

10y = 100

Divide both sides by 10

y = 100 ÷ 10

`\boxed{y = 10}`

∠C = 3y + 5

= 3*10 + 5

= 30 + 5

`\boxed{\bf \angle C = 35^\circ}`

∠D = 7y + 5

= 7*10 + 6

= 70 + 6

`\boxed{\bf \angle D = 76^\circ}`

∠C + ∠D + ∠DEC = 180° {Angle sum property of triangle}

35 + 76 + ∠DEC = 180

111 + ∠DEC = 180

∠DEC = 180 - 111

`\boxed{\bf \angle DEC = 69^\circ}`