Question

In δbcd, bd is extended through point d to point e, m∠cde = (6x-13)^{\circ}(6x−13) ∘ , m∠bcd = (2x + 10)°,, and m∠dbc = (x + 1)°.find m∠cde.

Answer 1

To find the measure of ∠CDE, set up an equation by using the fact that the sum of the angles in a triangle is 180°. Solve for x, and substitute the value back into the expression for ∠CDE.

Step-by-step explanation:

To find the measure of ∠CDE, we need to use the fact that the sum of the angles in a triangle is 180°. We can start by setting up an equation:

(2x + 10)° + (x + 1)° + (6x - 13)° = 180°

Combining like terms:

9x - 2 = 180°

Adding 2 to both sides:

9x = 182°

Dividing both sides by 9:

x = 20.22°

Now, we can substitute this value back into the expression for ∠CDE to find its measure:

(6(20.22) - 13)° = 107.32°