9514 1404 393
Answer:
k = 56°
Step-by-step explanation:
If b represents a base angle in an isosceles triangle, and 'a' represents the ap.ex angle, then the relation between them is ...
2b +a = 180°
from which we get ...
a = 180° -2b
b = (180° -a)/2
__
The angle at lower right is a base angle of the outside isosceles triangle. Its value is (180° -56°)/2 = 124°/2 = 62°.
The angle marked k is the ap.ex angle of the triangle whose base angle is 62°. We have already seen that the ap.ex angle is 180° -2(62°) = 56°.
k = 56°
_____
We don't see x anywhere on the diagram. The unmarked angle at lower left will be 62° -56° = 6°.
The obtuse angle on the right will be 180°-56°-6° = 118°. The acute angle of that linear pair is the other base angle of the smaller isosceles triangle, so is 62°.
