Question

Given the following diagram, find the missing measure.

Answer 1

The answer is D, b/c...

2x+5x= angle 4
7x= angle 4

Angle 4 and angle 1 form a supplementary angle, so:

180-7x= the measurement of angle 1.

Answer 2

we know that

The sum of the internal angles of the triangle is equal to $180$ degrees

in this problem we have

m∠2=$2x\°$

m∠3=$5x\°$

m∠1+m∠2+m∠3=$180\°$

Substitute the values and solve for m∠1

m∠1=$180\°-(2x+5x)\°$

m∠1=$180\°-7x\°$

Remember that

m∠1+m∠4=$180\°$ -------> by supplementary angles

Substitute the value of m∠1 and find m∠4

m∠4=$180\°-(180\°-7x\°)$

m∠4=$7x\°$

therefore

the answer is

a) the measure of m∠1=$180\°-7x\°$

b)  the measure of m∠4=$7x\°$