If m∠4 = 35, find m∠2. Explain. 35; ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.

145; ∠2 and ∠4 are supplementary angles, so m∠2 = 180 − m∠4.

55; ∠2 and ∠4 are complementary angles, so m∠2 = 90 − m∠4

35; ∠2 and ∠4 are corresponding angles, so m∠2 = m∠4.

A. 35; ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.

Given:

Required:

From the image given, angle 2 and angle 4 lie on opposite side of the line that intercepts the two parallel lines, AB and CD. Angle 2 and angle 4 both lie within the parallel lines. Therefore, are alternate interior angles.

Thus:

(alternate interior angles theorem)

Since,

therefore:

The right option is:

A. 35; ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.

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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.

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