In this diagram, lines AB and CD are parallel. Angle ABC measures 35° and angle BAC measures 115°.

What are the measures of the following angles?

1. m∠ACE = ___°

2. m∠DCB = ___°

3. m∠ACB = ___ °

1). m∠ACE = 115°

2). m(∠DCB) = 35°

3). m(∠ACB) = 30°

Step-by-step explanation:

In the diagram attached,

1). AB and CD are the parallel lines and the line AC is a transverse,

  m(∠ABC) = 35°

  m(∠BAC) = 115°

  ∠BAC ≅ ∠ACE [Alternate interior angles]

  m(∠ACE) = m(∠BAC) = 115°

2). Since, AB and CD are the parallel lines and line CB is a transverse,

   ∠ABC ≅ ∠DCB [Alternate interior angles]

    m(∠ABC) = m(∠DCB) = 35°

3). From ΔACB,

    m(∠ACB) + m(∠CBA) + m(BAC) = 180°

    m(∠ACB) + 35° + 115° = 180°

    m(∠ACB) = 30°

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