Given:
The right angled triangle is shown in the figure attached.
[tex]m\angle1=140\degree[/tex]
Required:
To find the measure of
[tex]m\angle3[/tex]
Explanation:
From the figure provided, we see that
[tex]\angle1[/tex]
and
[tex]\angle2[/tex]
are supplementary angles.
Therefore, the sum of measures of angles is 180.
Thus,
[tex]\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}[/tex]
Since the triangle is right angled triangle, one of the angles of a triangle is of measure
[tex]90\degree[/tex]
We know that the sum of measures of angles of a triangle is
[tex]180\degree[/tex]
Hence, the measure of angle 3 is given by,
[tex]\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}[/tex]
Final Answer:
