Question

Which equation can you use to solve for the value of x in the illustration shown?

Answer 1

x = 53°

Explanation:

Angles on straight line sum to 180°:

⇒ m∠ABD + 130° = 180°

⇒ m∠ABD = 50°

Interior angles of a triangle sum to 180°:

⇒ m∠ABD + m∠BDA+ m∠DAB = 180°

⇒ 50° + m∠BDA + 26° = 180°

⇒ m∠BDA + 76° = 180°

⇒ m∠BDA = 104°

Angles on straight line sum to 180°:

⇒ m∠BDA + m∠CDA = 180°

⇒ 104° + m∠CDA = 180°

⇒ m∠CDA = 76°

Interior angles of a triangle sum to 180°:

⇒ m∠CDA+ m∠DAC+ m∠ACD = 180°

⇒ 76°+ x + 51° = 180°

⇒ x + 127° = 180°

⇒ x = 53°