Question

22.The figure is not drawn to scale.If m<1 = 140, what is m<3?

Answer 1

Given:

The right angled triangle is shown in the figure attached.

`m\angle1=140\degree`

Required:

To find the measure of

`m\angle3`

Step-by-step explanation:

From the figure provided, we see that

`\angle1`

and

`\angle2`

are supplementary angles.

Therefore, the sum of measures of angles is 180.

Thus,

`\begin{gathered} m\angle1+m\angle2=180\degree \\ \Rightarrow140\degree+m\angle2=180\degree \\ \Rightarrow m\angle2=180\degree-140\degree \\ \Rightarrow m\angle2=40\degree \end{gathered}`

Since the triangle is right angled triangle, one of the angles of a triangle is of measure

`90\degree`

We know that the sum of measures of angles of a triangle is

`180\degree`

Hence, the measure of angle 3 is given by,

`\begin{gathered} m\angle2+90\degree+m\angle3=180\degree \\ \Rightarrow40\degree+90\degree+m\angle3=180\degree \\ \Rightarrow130\degree+m\angle3=180\degree \\ \Rightarrow m\angle3=180\degree-130\degree \\ \Rightarrow m\angle3=50\degree \end{gathered}`

Final Answer: