Question

Find the value of x, if C is on line AE

Answer 1

x = 11°

Step-by-step explanation:

• m∠C = m∠A = 33°

• m∠B = 2(x)

• m∠I = 180° - 5(x)

============ [ total interior angle in a triangle is 180° ]

solve for x

• 33° + 2(x) + 180° - 5(x) = 180°

• -3(x) = 180° - 213°

• -3(x) = -33°

• x = 11°

Answer 2

x = 11°

Step-by-step explanation:

Linear Pair

Two angles adjacent to each other that form a straight line.

The sum of angles of a linear pair is always equal to 180°.

⇒ m∠C = 180° - 33° = 147°

Alternate Interior Angle Theorem

When two parallel lines are cut by a transversal, the alternate interior angles are congruent.

From inspection of the diagram, we can see that AB ║ DC.

Therefore, AE is the transversal.

So m∠A = 33°

Sum of interior angles of a triangle is 180°

Therefore, the top angle of the triangle = 180° - m∠A - 2x

= 180° - 33° - 2x

= 147° - 2x

Angles around a point add up to 360°

⇒ 33° + m∠C + 5x + (147° - 2x) = 360°

⇒ 33° + 147° + 5x + 147° - 2x = 360°

⇒ 327° + 3x = 360°

⇒ 3x = 33°

⇒ x = 11°