Question

In the figure, ABCE is a parallelogram, CDE is an equilateral triangle and BCD is a straight line.

Answer 1

$\begin{gathered} \angle P\text{ = 60} \\ \angle q\text{ = 120} \\ \angle r\text{ = 120} \\ \angle s\text{ = 60} \end{gathered}$

Mathematically, the sum of angles in a triangle is 180

The angles in an equilateral triangle are equal and that means each of the angle measure is 60 degrees each

Since the measure of angle P is in the equilateral triangle, we have it that the measure of angle P is 60 degrees

Now, we can see that q and p lie on a straight line

Mathematically, the sum of angles in a straight line is 180

This mean that the two angles sum up to be 180

Thus;

$\angle q\text{ = 180-}\angle p\text{ = 180-60 = 120}$

For a parallelofgram, angles that are directly opposite on the diagonal stretch are equal

This means that r is equal to q which is 120

Lastly, angles that are on same base are supplementary

That means s added to q will give 180

So, we have it that;

$\begin{gathered} s\text{ = 180-m}\angle q \\ s\text{ = 180-120 = 60} \end{gathered}$