Question

If m∠4 = 35, find m∠2. Explain.

Answer 1

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

Triangle CAB is a right triangle.

Therefore, m∠1 = 90°

Similarly, m∠ACD = 90°

m∠ACD = m∠ACB + m∠BCD = 90°

             = m∠3 + m∠4 = 90°

Since m∠4 = 35°,

m∠3 + 35° = 90°

m∠3 = 90° - 35°

        = 55°

In the triangle ABC,

m∠ACB + m∠CBA + m∠BAC = 180° [Property of a triangle]

m∠3 + m∠2 + m∠1 = 180°

55° + m∠2 + 90° = 180°

m∠2 + 145° = 180°

m∠2 = 180° - 145°

        = 35°

Since, AB║CD and BC is a transverse,

Therefore, m∠2 = m∠4 = 35° [Alternate interior angles]

Option (1) is the correct option.