NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Properties of quadrilaterals

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Required skills (click to reveal)

In quadrilateral ABCD, AB is parallel to DC and AD is parallel to BC, making ABCD a parallelogram. Diagonal AC bisects angle A, and angle A is 59 degrees.

What is the exact measure, in degrees, of angle BAC? Use the properties of parallelograms and angle bisectors to determine the answer.

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Squares belong to two broader families. A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.RectangleRhombusSquare
A square is both a rectangle and a rhombus. The arrows mean “is a type of”, not a step in a calculation.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. Given that ABCD is a parallelogram, opposite sides are parallel: AB || DC and AD || BC.
  2. Angle A is given as 59 degrees, and diagonal AC bisects angle A.
  3. Since AC bisects angle A, it divides angle A into two equal parts: angle BAC = angle CAD.
  4. Therefore, angle BAC = 59° / 2 = 29.5°.
  5. This result follows from the definition of an angle bisector: it splits an angle into two congruent angles.
  6. No further geometric properties of the parallelogram are needed to find angle BAC, as the bisector directly divides angle A.
  7. The value 29.5° is exact and does not require rounding.
  8. Check: 29.5° + 29.5° = 59°, which matches angle A.
  9. The solution is consistent with the properties of angle bisectors and parallelograms.
  10. Angle BAC is exactly half of angle A, so 59° ÷ 2 = 29.5°.
  11. The measure of angle BAC is 29.5 degrees.
  12. Final answer confirmed: 29.5° is correct and matches the required format.

Reference answer: 29.5

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