Q14. - Geometry

Question

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

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

Step-by-Step Solution

Answer

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

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 ∠ D X C .

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

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

Step 3. Determine the value of m ∠ C X B .

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 $m\angle CXB$.

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