Question

One of the exterior angles of an isosceles triangle is 150°. What is the ratio of its unequal interi
angles in same triangle ?
(1) 1:4
(2) 5:2
(3) either (1) or (2) (4) Can't say
AF : FC = 3:4 and BC: AE = 2:3. then find the ratio of the area of AECD to
IFB.​

Answer 1

Given :  One of the exterior angles of an isosceles triangle is 150°.

To Find : ratio of its Equal angle with unequal interior angle    in same triangle

1) 1:4

(2) 5:2

(3) either (1) or (2)

(4) Can't say

Solution:

Case 1 : exterior angles of an isosceles triangle is 150°. is with  unequal angle

then unequal angle  = 180° - 150° = 30°

and equal angles = ( 180°  - 30°)/2  = 75°

Ratio is  75° :  30°

= 5 : 2

Case 2 : exterior angles of an isosceles triangle is 150°.  with   equal angle

equal angle  = 180° - 150° = 30°

and unequal angles =  180°  - 2 * 30° = 120°

30° : 120°

= 1 : 4

(3) either (1) or (2)  is correct option  

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