Answer:
The value of y° = 80°
Explanation:
Given
m∠A = 20
m∠B = x°
as
x = 100,
so
m∠B = 100
We know that the sum of angles of a triangle is 180°.
Thus, the m∠C of the triangle ABC can be calculated as:
m∠A + m∠B + m∠C = 180°
20° + 100° + m∠C = 180°
m∠C = 180° - 120°
= 60°
As we know that Vertical angles are always congruent.
In other words, m∠C is common in both triangles ΔABC and ΔCDE
m∠C = 60°
m∠E is also given.
i.e. m∠E = 40°
as
m∠D = y°
So, we have to determine m∠D in order to determine y°.
We know that the sum of angles of a triangle is 180°.
Thus, using the values of the angles ΔCDE
i.e.
m∠C + m∠D + m∠E = 180°
60° + y° + 40° = 180°
y° = 180° - 100°
y° = 80°
Therefore, the value of y° = 80°