In rhombus ABCD, angle A = 31 degrees. The diagonals intersect point O. Find the angles of the triangle angle BOC.
February 4, 2021 | education
| To solve problems of this type, the main thing is to know this property of the diagonals of a rhombus. They intersect at right angles and are bisectors of the corners of the rhombus.
By condition, angle A = 31 °, angle A = angle C.
Consider a BOC right-angled triangle, the corners of which we need to find:
BOC angle = 90 ° (diagonals are perpendicular).
Angle ВСО = 31 ° / 2 = 15.5 ° (diagonals – bisectors).
CВO angle = 90 ° – 15.5 ° = 74.5 °.
Answer: The angles of the ВOC triangle have a degree measure: 15.5 °, 74.5 °, 90 °.
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