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Find the value of the missing angle.

Mathematics

ScanSolve AI Answer

Answer

48∘\mathbf{48^\circ}

Step-by-step solution

4 steps
  1. Identify the parallel lines and the angles.

    The horizontal lines are parallel. We have a zigzag transversal intersecting these parallel lines.
    The angles given are x∘x^\circ, 78∘78^\circ, and 30∘30^\circ.

  2. Apply the "angles pointing left = angles pointing right" rule (also known as the "M" rule or zigzag rule).

    This rule states that for a zigzag line between two parallel lines, the sum of the angles pointing in one direction is equal to the sum of the angles pointing in the opposite direction.

    • Angles pointing to the right: x∘x^\circ and 30∘30^\circ.
    • Angles pointing to the left: 78∘78^\circ.
  3. Set up the equation based on the rule.

    x∘+30∘=78∘x^\circ + 30^\circ = 78^\circ
  4. Solve for xx.

    x=78−30x = 78 - 30 x=48x = 48

    The value of xx is:

    48∘\mathbf{48^\circ}
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