Question

If m∠BOC = (3x + 1)° and m∠COD = (11x − 3)°, what is m∠COD?
13°
40°
69°
140°

Answer 1

The correct answer is:

140°

If m∠BOC = (3x + 1)° and m∠COD = (11x − 3)°, then the measure of angle COD is 140°. This can be determined by substituting the given values for the measures of angles BOC and COD into the equation m∠COD = m∠BOC + m∠COD. This gives us the following equation:

m∠COD = (3x + 1)° + (11x − 3)°

Solving for m∠COD, we get:

m∠COD = 14x − 2

Substituting the given value for x, we get:

m∠COD = 14(10) − 2 = 140°

Therefore, the measure of angle COD is 140°.

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Answer 2

Answer:

D)  140°

Step-by-step explanation:

Angles BOC and COD form a linear pair.

Therefore, the sum of the two angles is 180°.

⇒ m∠BOC + m∠COD = 180°

⇒ (3x + 1)° + (11x - 3)° = 180°

⇒ 3x + 1 + 11x - 3 = 180

⇒ 3x + 11x + 1 - 3 = 180

⇒ 14x - 2 = 180

⇒ 14x - 2 + 2 = 180 + 2

⇒ 14x = 182

⇒ 14x ÷ 14 = 182÷ 14

⇒ x = 13

To find the measure of angle COD, substitute the found value of x into the expression for m∠COD:

⇒ m∠COD = (11x - 3)°

⇒ m∠COD = (11 · 13 - 3)°

⇒ m∠COD = (143 - 3)°

⇒ m∠COD = 140°