Question

Help me to find the measure of angles 1 2 and 3!

Answer 1

Given:

Given the diagram

Required: The measure of angles 1, 2 and 3.

Step-by-step explanation:

The sum of interior angles of a triangle is 180 degrees. So,

`\begin{gathered} x+55^o+70^o=180^o \\ x=180^o-55^o-70^o \\ =55\degree \end{gathered}`

The angles x and 1 are supplementary angles, that is, the sum of angles 1 and x gives 180 degrees.

`\begin{gathered} x+m\angle1=180\degree \\ 55\degree+m\angle1=180\degree \\ m\angle1=180\degree-55\degree \\ =125\degree \end{gathered}`

The angle 2 is the opposite angle of 55 degrees. Hence angle 2 equals 55 degrees, that is,

`m\angle2=55\degree`

Angle y and 150 degrees are supplementary angles. So,

`\begin{gathered} y+150\degree=180\degree \\ y=180\degree-150\degree \\ =30\degree \end{gathered}`

The sum of the interior angles of a triangle equals 180 degrees.

`\begin{gathered} m\angle2+m\angle3+y=180\degree \\ 55\degree+m\angle3+30\degree=180\degree \\ m\angle3=180\degree-55\degree-30\degree \\ =95\degree \end{gathered}`

Final Answer:

`m\angle1=125\degree,m\angle2=55\degree,m\angle3=95\degree`