The straight line joins the midpoint of the two adjacent sides of the rhombus.
Therefore, the two sides of the triangle formed are equal too and according to the Isosceles triangle property the two angles are equal too
Let the two angle be x.
We know,
In rhombus opposite angle are equal. So, the third angle of the triangle = 80°
Now, Sum of angles of a triangle = 180°
x + x + 80° = 180°
2x + 80° = 180°
2x = 100°
x = 50°
The angles of the triangle formed are 50°, 50° and 80°.
As a is an external angle of the triangle and external angle of a triangle is the sum of the two opposite sides, We get :
a = 80° + 50°
a = 130°