Advertisements
Advertisements
Question
The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.
Advertisements
Solution
\[\text{ Draw a parallelogram ABCD } . \]
\[\text{ Drop a perpendicular from B to the side AD, at the point E } . \]
\[\text{ Drop perpendicular from B to the side CD, at the point F } . \]
\[\text{ In the quadrilateral BEDF }: \]
\[\angle EBF = 60°, \angle BED = 90°\]
\[\angle BFD = 90°e \]
\[\angle EDF = 360° - (60° + 90° + 90°) = 120°\]
\[\text{ In a parallelogram, opposite angles are congruent and adjacent angles are supplementary } . \]
\[\text{ In the parallelogram ABCD }: \]
\[\angle B = \angle D = 120° \]
\[\angle A = \angle C = 180°e - 120° = 60 °\]
RELATED QUESTIONS
Explain why a rectangle is a convex quadrilateral.
ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you)
Which of the following statement is true for a rectangle?
It has two pairs of equal sides.
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
A mason has made a concrete slab. He needs it to be rectangular. In what different ways can he make sure that it is rectangular?
Prove that quadrilateral formed by the intersection of angle bisectors of all angles of a parallelogram is a rectangle.
Show that the bisectors of angles of a parallelogram form a rectangle
For which of the following figures, diagonals are equal?
In rectangle READ, find ∠EAR, ∠RAD and ∠ROD
In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA.
