Q15. - Geometry

Question

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

If $m\angle DAX=70$, find the measure of $\angle XAB$.

Step-by-Step Solution

Answer

The value of $m\angle XAB=20°$.

Step 1. Observe the given figure.

The $\angle DAX$ represents itself as the part of $\angle DAB$ and the value of $m\angle DAB=90°$. The $\angle XAB$ is another part of $\angle DAB$.

Step 2. Make an equation by using the observation.

As both the angles $\angle DAX$ and $\angle XAB$ represents itself as the part of $\angle DAB$ so it can be said that the addition of these two angles will be equal to $\angle DAB$. By using this information make an equation.

$m\angle DAX+m\angle XAB=90°$

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

Substitute the given value of $m\angle DAX$ into the obtained equation after it perform the simplification.

$$\begin{gathered} 70°+m\angle XAB=90° \\ m\angle XAB=90°-70° \\ m\angle XAB=20° \end{gathered}$$