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प्रश्न
Find the angles marked with a question mark shown in Fig. 17.27
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उत्तर
\[\text{ In } \bigtriangleup CEB: \]
\[\angle ECB + \angle CBE + \angle BEC = 180° (\text{ angle sum property of a triangle })\]
\[40° + 90° + \angle EBC = 180° \]
\[ \therefore \angle EBC = 50° \]
\[\text{ Also }, \angle EBC = \angle ADC = 50° \left( \text{ opposite angle of a parallelogram } \right)\]
\[\text{ In } \bigtriangleup FDC: \]
\[\angle FDC + \angle DCF + \angle CFD = 180° \]
\[50° + 90° + \angle DCF = 180° \]
\[ \therefore \angle DCF = 40° \]
\[\text{ Now }, \angle BCE + \angle ECF + \angle FCD + \angle FDC = 180° (\text{ in a parallelogram, the sum of alternate angles is } 180° )\]
\[50° + 40° + \angle ECF + 40° = 180° \]
\[\angle ECF = 180° - 50° + 40° - 40° = 50° \]
संबंधित प्रश्न
The following figure is parallelogram. Find the degree values of the unknown x, y, z.
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
In a parallelogram ABCD, ∠D = 135°, determine the measure of ∠A and ∠B.
Diagonals of parallelogram ABCD intersect at O as shown in the following fegure. XY contains O, and X, Y are points on opposite sides of the parallelogram. Give reasons for each of the following:
(i) OB = OD
(ii) ∠OBY = ∠ODX
(iii) ∠BOY = ∠DOX
(iv) ∆BOY ≅ ∆DOX
Now, state if XY is bisected at O.
Which of the following statement is true for a rhombus?
Its diagonals bisect each other at right angles.
Which of the following statement is true for a rhombus?
It is a quadrilateral.
ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal BD = 16 cm, find the length of diagonal AC.
If the diagonal of a rhombus are equal, then the rhombus is a
If the adjacent sides of a parallelogram are equal then parallelogram is a ______.
ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Find the angles of the rhombus.
Hint: Join BD. Then ∆ABD is equilateral.
