Question

if (mangle bce=x), and the (mangle dce) is 4 times bigger than (mangle bce), then find (x) and (mangle dce). (mangle dcb = 130)

Explanation:

Step1: Express m∠DCE in terms of x

Since m∠DCE is 4 times bigger than m∠BCE and m∠BCE = x, then m∠DCE = 4x.

Step2: Use the angle - addition postulate

We know that m∠DCB=m∠DCE + m∠BCE. Given m∠DCB = 130, we substitute the expressions for m∠DCE and m∠BCE into the equation: 4x+x=130.

Step3: Combine like - terms and solve for x

Combining like - terms, we get 5x = 130. Dividing both sides by 5, we have x=\frac{130}{5}=26.

Step4: Find m∠DCE

Since m∠DCE = 4x and x = 26, then m∠DCE=4×26 = 104.

Answer:

x = 26
m∠DCE = 104