Question

Given the following diagram, find the missing measure.

m∠2 = 2x°, m∠3 = 5x°, m∠1 =

A.2x + 5x
B.5x - 2x
C.180 - 5x
D.180 - 7x

Answer 1

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\°`

Answer 2

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.