Saved Bookmarks
| 1. |
In the given figure, AB = AC,BC = CD and DE∥BC . If ∠FAE= 122° and ∠CDE= x° Find total number of factor of x |
|
Answer» ∠EAD = 180 - ∠FAE (Linear pair) = 180 - 122 = 58° Now AB = AC, So ∠ABC = ∠ACB In triangle ABC, 2∠ABC = 180 - ∠EAD (Angle sum property) 2∠ABC = 122 ∠ABC = ∠ACB = 61° Again, CD = BC ∠ABC = ∠CDB = 61° In triangle, CDB 2∠CDB = 180 - ∠DCB ∠DCB = 58° It is given that DE ∥ BC, so ∠x = ∠DCB = (Alternate angles) ∠x = 58° No of factors of 58 are 1,2, 29 and 58. Hence, the total numbers of factors of x are 4. |
|