Question

given: (mangle acd = mangle bdc), (mangle1 = mangle3) prove: (mangle2 = mangle4) statements a. (mangle acd = mangle bdc), (mangle1 = mangle3) b. (mangle acd=mangle1 + mangle2) (mangle bcd = mangle3 + mangle4) c. reasons a. b. c.

Explanation:

Step1: State given information

Given that $m\angle ACD = m\angle BDC$ and $m\angle1 = m\angle3$.

Step2: Use angle - addition postulate

By the angle - addition postulate, $m\angle ACD=m\angle1 + m\angle2$ and $m\angle BDC=m\angle3 + m\angle4$.

Step3: Substitute equal angles

Since $m\angle ACD = m\angle BDC$ and $m\angle1 = m\angle3$, we substitute: $m\angle1 + m\angle2=m\angle3 + m\angle4$.

Step4: Subtract equal angles from both sides

Subtract $m\angle1$ (which is equal to $m\angle3$) from both sides of the equation $m\angle1 + m\angle2=m\angle3 + m\angle4$. We get $m\angle2=m\angle4$.

Answer:

$m\angle2 = m\angle4$