Question

Given the diagram, tell whether you can reach the conclusion shown.

If $m\angle 1=46$, find $m\angle DXC$and $m\angle CXB$.

Short answer

The value of $m\angle DXC=134$and$m\angle CXB=46$.

Step-by-step solution

Step 1. Look for the suitable method.

The postulate 4 is the suitable method according to which the measurement of straight angle is $180°$.

Step 2. Determine the value of m∠DXC.

Both the angles $m\angle DXC$and $\angle 1$are present on a straight line $\overline{AC}$which means that the addition of localid="1649228650652" $m\angle DXC$and $\angle 1$will be equal to $180°$. Using this determine the value of $m\angle DXC$.

localid="1649228825414" $$\begin{gathered} m\angle 1+m\angle DXC=180 \\ 46+m\angle DXC=180 \\ m\angle DXC=180-46 \\ m\angle DXC=134 \end{gathered}$$

Step 3. Determine the value of m∠CXB.

Both the angles $m\angle DXC$and $m\angle CXB$are present on a straight line $\overline{BD}$which means that the addition of $m\angle DXC$and $\angle 1$will be equal to $180°$. Using this determine the value of $m\angle CXB$.

localid="1649230592504" $$\begin{gathered} m\angle DXC+m\angle CXB=180 \\ 134+m\angle CXB=180 \\ m\angle CXB=180-134 \\ m\angle CXB=46 \end{gathered}$$