In rhombus ABCD, the diagonals intersect at point O. Angle A = 31 °. Find the angles of the triangle BOC.
| September 9, 2021 | education
Given: ABCD is a rhombus whose diagonals intersect at point O. Angle A = 31 °.
Find: Angles of triangle BOC.
Solution:
In a rhombus, angle A will be equal to angle C and will be equal to 31 °.
Since the diagonals of the rhombus are bisectors, the angle BCA = 31/2 = 15.5 °.
The diagonals of the rhombus are perpendicular, that is, they intersect at right angles, so the BOC angle will be 90 °. Then the angle OBC will be equal to the difference between the angle BOC and BCA.
OBC angle = 90 – 15.5 = 74.5 °.
Answer: BCA angle = 15.5 °, BOC angle = 90 °, OBC angle = 74.5 °.
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