Question

Match the following with the value of X.

• A. 45°
• B. 75°
• C. 60°

Answer 1

In all the figures, line DE and BC are parallel.

In the first figure,
$\angle ADE$ and $\angle ABC$ are corresponding angles.
We know that the corresponding angles are equal. So, $\angle ADE=\angle ABC=45°$
$\Rightarrow x=45°.$

In the second figure,
In $△ADE,$
$\angle ADE+\angle DEA+\angle EAD=180°$ [Angle Sum Property]
$\Rightarrow \angle AED=180-60-45=75°$
$\angle AED$ and $\angle ACB$ are corresponding angles, so $\angle ACB=75°$
$\Rightarrow x=75°.$

In the third figure,
$\angle BDE=120°$
It is clear from the figure that line BD is transversal to the parallel lines DE and BC.
So, $\angle BDE$ and $\angle ABC$ are interior angles on the same side of the transversal and thus, they are supplementary.
Hence, $\angle ABC=180-120=60°$
$\Rightarrow x=60.°$