Final answer:
To find the value of 'a', you can use the fact that the sum of the angles in a triangle is 180°. By setting up and solving equations using this fact, you can determine that the value of 'a' is 40°.
Step-by-step explanation:
To find the value of a, we can use the fact that the sum of the angles in a triangle is 180°. Since m∠BCE = m∠DCE = 40°, we have:
40° + 40° + m∠CED = 180°
Simplifying the equation, we get:
m∠CED = 180° - 40° - 40°
m∠CED = 100°
Since the angle ∠CED is shared between two congruent sides, BE and DE, we can use the fact that the sum of the angles in a triangle is 180° to find the value of a. We can set up the following equation:
40° + m∠CDE + m∠CED = 180°
Substituting the value of m∠CED that we found earlier, we get:
40° + m∠CDE + 100° = 180°
Simplifying the equation, we have:
m∠CDE = 180° - 40° - 100°
m∠CDE = 40°
Since ∠BCE and ∠CDE are vertical angles, they are congruent. This means that we can set up the following equation:
40° = m∠BCE = m∠CDE
Since angles BCE and CDE are congruent, we can set up another equation using the fact that the sum of the angles in a triangle is 180°:
40° + 40° + m∠ECD = 180°
Simplifying the equation, we get:
m∠ECD = 180° - 40° - 40°
m∠ECD = 100°
Since angle ∠ECD is congruent to angle ∠DCE, we have:
m∠ECD = m∠DCE = 40°
Therefore, the value of a is 40°.