Question

FIND THE MEASURE OF EACH ANGLE<1 and <2 are supplementary. <2 and <3 are supplementary. m<1= 133 degrees.

Answer 1

When two angles are suplementary the sum of their measurements must be equal to 180 degrees. We know that angles 1 and 2 are suplementary, as well as angles 2 and 3, therefore:

`\begin{gathered} \measuredangle1+\measuredangle2=180 \\ \measuredangle2+\measuredangle3=180_{} \end{gathered}`

We know the value of angle 1, therefore we can find the angle 2 by replacing it by its value on the first equation.

`\begin{gathered} 133+\measuredangle2=180 \\ \measuredangle2=180-133 \\ \measuredangle2=47 \end{gathered}`

With the value of the angle 2 we can find the value of 3, by replacing it on the second equation.

`\begin{gathered} 47+\measuredangle3=180 \\ \measuredangle3=180-47 \\ \measuredangle3=133 \end{gathered}`

The angle one measures 133 degrees.

The angle two measures 47 degrees.

The angle three measures 133 degrees.