Answer
The measure of angle 1 is \[~35{}^\circ \].
Work Step by Step
In the present case, there is a triangle having two of its exterior angles as \[65{}^\circ \] and \[100{}^\circ \]. To find the measure of angle 1, first find the interior angles of the triangle with the help of its exterior angles.
Let the interior vertical angle of exterior vertical angle \[65{}^\circ \] is \[\measuredangle a\].The measure of \[\measuredangle a\]can be ascertained using the property of vertical angles that states that vertical angles are equal. Since \[\measuredangle a\] and \[65{}^\circ \]are vertical angles. Accordingly, \[m\measuredangle a=65{}^\circ \].
Now, let the interior angle of exterior angle \[100{}^\circ \] is \[\measuredangle b\]. The measure of \[\measuredangle b\] can be ascertained using the property of straight line that states that sum of all angles on a straight line is \[180{}^\circ \].
Accordingly compute the measure of angle b using the equation as shown below:
\[\begin{align}
& m\measuredangle b+100{}^\circ =180{}^\circ \\
& m\measuredangle b=180{}^\circ -100{}^\circ \\
& m\measuredangle b=80{}^\circ
\end{align}\]
Now, measure of angle 1 can be ascertained by using the property of sum of angles of a triangle that states that sum of angles of a triangle is \[180{}^\circ \].
Now, compute the measure of angle 1 using the equation as shown below:
\[\begin{align}
& m\measuredangle 1+65{}^\circ +80{}^\circ =180{}^\circ \\
& m\measuredangle 1+145{}^\circ =180{}^\circ \\
& m\measuredangle 1=180{}^\circ -145{}^\circ \\
& m\measuredangle 1=35{}^\circ
\end{align}\]
Hence, the measure of \[m\measuredangle 1\] is \[~35{}^\circ \].
