Question

If the m angle 1 is (6x-2) and then the m angle 3 is (10x-30) the find the measure of angle 1

Answer 1

Step-by-step explanation:

Given:

m<1= 6x-2

m<3 = 10x-30

Based on the given figure, angles 1 and 3 are vertical, so they are equal. Vertical angles are angles opposite each other and are always congruent.

So,

m<1=m<3

We plug in what we know.

`\begin{gathered} m<1=m<3 \\ 6x-2\text{ = 10x-30} \\ \text{Simplify and rearrange} \\ 10x-6x=-2+30 \\ 4x=28 \\ x=(28)/(4) \\ \text{Calculate} \\ x=7 \end{gathered}`

Then, we plug in x=7 into m<1= 6x-2.

`\begin{gathered} m<1=6x-2 \\ =6(7)-2 \\ =42-2 \\ m<1=40 \end{gathered}`

We can also double check it on m<3. We plug in x=7 into 10x-30. So,

m<3 = 10x-30=10(7)-30 = 40°.

Therefore