#1**+5 **

I'm not sure, but I think x is 30 degrees and y is 40 degrees.

(If you want an explanation, then you can ask. The reason why I didn't give one, is I'm not too sure.)

IhaveOBJD Feb 6, 2021

#2**+1 **

There might be a better way to determine those angles – there probably is a better way to determine those angles – but here's what I thought of.

Move to the left of the angle marked 3y and draw a perpendicular between lines e and f.

This creates a five sided figure. The sum of the interior angles of a polygon of n sides is (n – 2) • 180^{o}

The sum of the interior angles of the pentagon is 540^{o}

Note that one of the interior angles is the supplementary angle of 2x so its value is (180^{o} – 2x)

The five angles:

**90 ^{o}** - one of the angles newly created with the perpendicular line

**90 ^{o}** - the other angle newly created with the perpendicular line

**3y** - another angle

**(180 ^{o} – 2x)** - another angle

**a** - the angle we want to find

a = 540^{o} minus all the other angles

a = 540^{o} – 90^{o} – 90^{o} – 3y – (180^{o} – 2x)

a = 540^{o} – 180^{o} – 3y – 180^{o} + 2x

**a = 2x – 3y + 180 ^{o}**

_{.}

Guest Feb 6, 2021