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प्रश्न
In the adjacent figure HOPE is a parallelogram. Find the angle measures x,y and z. State the geometrical truths you use to find them.
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उत्तर
\[\angle HOP + 70°= 180° (\text{ linear pair })\]
\[\angle HOP = 180°- 70°= 110°\]
\[x = \angle HOP = 110° (\text{ opposite angles of a parallelogram are equal })\]
\[\angle EHP + \angle HEP = 180°(\text{ sum of adjacent angles of a parallelogram is } 180°)\]
\[110° + 40° + z = 180°\]
\[z = 180° - 150°= 30°\]
\[y = 40° \left( \text{ alternate angles }\right)\]
संबंधित प्रश्न
The following figure is parallelogram. Find the degree values of the unknown x, y, z.
Can the following figure be parallelogram. Justify your answer.
The measure of one angle of a parallelogram is 70°. What are the measures of the remaining angles?
Two adjacent sides of a parallelogram are 4 cm and 3 cm respectively. Find its perimeter.
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
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It is a parallelogram.
ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal BD = 16 cm, find the length of diagonal AC.
In a rhombus PQRS if PQ = 7.5 cm then find QR. If ∠QPS = 75° then find the measure of ∠PQR and ∠SRQ.
State with reason whether the following statement is ‘true’ or ‘false’.
Every parallelogram is a rhombus.
If all pairs of adjacent sides of a quadrilateral are congruent then it is called ______.
