Answer
Measurement of angle 1 and angle 2 is\[65{}^\circ \]each respectively, angle 3 is\[50{}^\circ \] and measurement of angle 4 and angle 5 is \[115{}^\circ \] and \[65{}^\circ \]each, respectively.
Work Step by Step
Compute angle 1 using the fact that angles \[115{}^\circ \] and angle 1 form a straight angle. Therefore, their sum is equal to\[180{}^\circ \] as shown below:
\[m\angle 1+115{}^\circ =180{}^\circ \]
Compute the measurement of angle 1 by subtracting \[{{115}^{{}^\circ }}\]from both the sides of equation as shown below:
\[\begin{align}
& m\angle 1=180{}^\circ -115{}^\circ \\
& m\angle 1=65{}^\circ \\
\end{align}\]
Compute the measurement of angle 2 using the fact that angles opposite to the equal sides of isosceles triangle are equal as shown below:
\[\begin{align}
& m\angle 1=m\angle 2 \\
& m\angle 2=65{}^\circ \\
\end{align}\]
According to angle sum property, the sum of all the three angles of a triangle is\[180{}^\circ \]. Compute the measure of angle 2 as follows:
Simplify the equation by substituting the given values as follows:
\[\begin{align}
& 65{}^\circ +65{}^\circ +m\angle 3=180{}^\circ \\
& m\angle 3+130{}^\circ =180{}^\circ
\end{align}\]
Compute the measurement of angle 3 by subtracting \[{{130}^{{}^\circ }}\]from both the sides of equation as shown below.
\[\begin{align}
& m\angle 3=180{}^\circ -130{}^\circ \\
& m\angle 3=50{}^\circ \\
\end{align}\]
Compute the measurement of angle 4 using the fact that angles 2 and 4 form a straight angle. Therefore, their sum is equal to\[{{180}^{\circ }}\].
\[m\angle 2+m\angle 4=180{}^\circ \]
Simplify the equation by substituting the given values as follows:
\[65{}^\circ +m\angle 4=180{}^\circ \]
Compute the measurement of angle 4 by subtracting \[65{}^\circ \]from both the sides of equation as shown below:
\[\begin{align}
& m\angle 4=180{}^\circ -65{}^\circ \\
& m\angle 4=115{}^\circ \\
\end{align}\]
Compute the measurement of angle 5 using the fact that vertically opposite angles are equal to each other as shown below:
\[\begin{align}
& m\angle 5=m\angle 2 \\
& m\angle 5=65{}^\circ \\
\end{align}\]
