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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
In the following figure GUNS and RUNS are parallelogram. Find x and y.
In the following Figure ABCD is a arallelogram, CE bisects ∠C and AF bisects ∠A. In each of the following, if the statement is true, give a reason for the same:
(i) ∠A = ∠C
(ii) \[\angle FAB = \frac{1}{2}\angle A\]
(iii) \[\angle DCE = \frac{1}{2}\angle C\]
(iv) \[\angle CEB = \angle FAB\]
(v) CE || AF
In a parallelogram ABCD, AB = 10 cm, AD = 6 cm. The bisector of ∠A meets DC in E, AEand BC produced meet at F. Find te length CF.
Which of the following statement is true for a rhombus?
Its diagonals bisect each other at right angles.
Fill in the blank, inthe following, so as to make the statement true:
A rhombus has all its sides of ...... length.
Fill in the blank, in the following, so as to make the statement true:
The diagonals of a rhombus ...... each other at ...... angles.
Show that each diagonal of a rhombus bisects the angle through which it passes.
If a diagonal of a quadrilateral bisects both the angles, then it is a ______.
If all sides of a quadrilateral are equal, it is a ______.
Construct a rhombus CLUE in which CL = 7.5 cm and LE = 6 cm.
