Answer
The measurement of angle BGD is equal to 90°
Work Step by Step
Let the measure of AGB is x and therefore, the measure of BGC will be x. Let the measure of CGD is y and therefore, the measure of DGE is y.
Now as it can be seen from the figure that the AGB, BGC, CGD, and DGE are together constituting straight angle and the sum of a straight angle is 180°, therefore, the sum of these angles will be 180°.
\[\begin{align}
& \measuredangle AGB+\measuredangle BGC+\measuredangle CGD+\measuredangle DGE=180{}^\circ \\
& x+x+y+y=180{}^\circ \\
& 2x+2y=180{}^\circ \\
& 2\times \left( x+y \right)=180{}^\circ
\end{align}\]
\[\begin{align}
& x+y=\frac{180{}^\circ }{2} \\
& =90{}^\circ
\end{align}\]
Thus, \[\measuredangle BGC+\measuredangle CGD\]is equal to 90° and similarly, \[\measuredangle AGB+\measuredangle DGE\]is equal to 90°
Now, it is required to find the measure of angle BGD. The angle BGD is the sum of angle BGC and angle CGD Thus, the measure of \[\measuredangle \text{BGD}\]can be computed as follows:
\[\begin{align}
& \measuredangle \text{BGD}=\measuredangle \text{BGC}+\measuredangle \text{CGD} \\
& =x+y \\
& =90{}^\circ
\end{align}\]
Thus, the measure of \[\measuredangle BGD\]is 90°.
