Answer
Measurement of angle 1 is\[50{}^\circ \], angle 2 is\[50{}^\circ \], angle 3 is\[80{}^\circ \], angle 4 is\[130{}^\circ \]and angle 5 is\[130{}^\circ \].
Work Step by Step
Compute angle 1 using the fact that angles \[130{}^\circ \] and angle 1 form a straight angle. Therefore, their sum is equal to\[180{}^\circ \].
\[130{}^\circ +m\measuredangle 1=180{}^\circ \]
Compute the measurement of angle 1 by subtracting \[{{130}^{{}^\circ }}\]from both the sides of equation.
\[\begin{align}
& m\measuredangle 1=180{}^\circ -130{}^\circ \\
& m\angle 1=50{}^\circ \\
\end{align}\]
Compute the measurement of angle 2 using the fact that angles opposite to the equal sides of isosceles triangle are equal as shown below.
\[\begin{align}
& m\angle 1=m\angle 2 \\
& m\angle 2=50{}^\circ \\
\end{align}\]
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:
Sum of all the three angels of a triangle is\[{{180}^{\circ }}\]as shown below.
\[m\angle 1+m\angle 2+m\angle 3=180{}^\circ \]
Simplify the equation by substituting the given values as follows:
\[\begin{align}
& 50{}^\circ +50{}^\circ +m\angle 3=180{}^\circ \\
& m\measuredangle 3+100{}^\circ =180{}^\circ
\end{align}\]
Compute the measurement of angle 3 by subtracting \[{{100}^{{}^\circ }}\]from both the sides of equation as shown below.
\[\begin{align}
& m\angle 3=180{}^\circ -100{}^\circ \\
& m\angle 3=80{}^\circ \\
\end{align}\]
Compute the measurement of angle 4 using the fact that angles 2 and 4 form a straight angle. Therefore, their sum is equal to\[{{180}^{\circ }}\]as shown below:
\[m\measuredangle 2+m\sphericalangle 4=180{}^\circ \]
Simplify the equation by substituting the given values as follows:
\[50{}^\circ +m\angle 4=180{}^\circ \]
Compute the measurement of angle 4 by subtracting \[{{50}^{{}^\circ }}\]from both the sides of equation as shown below.
\[\begin{align}
& m\angle 4=180{}^\circ -50{}^\circ \\
& m\angle 4=130{}^\circ \\
\end{align}\]
Compute the measurement of angle 5 using the fact that vertically opposite angles are equal to each other as shown below.
\[\begin{align}
& m\angle 5=m\angle 4 \\
& m\angle 5=130{}^\circ \\
\end{align}\]