Answer
The measurement of angle 1 is \[55{}^\circ \], angle 2 is \[65{}^\circ \], angle 3 is \[60{}^\circ \], angle 4 is \[65{}^\circ \], angle 5 is \[60{}^\circ \], angle 6 is \[120{}^\circ \], angle 7 is \[60{}^\circ \], angle 8 is \[60{}^\circ \], angle 9 is \[55{}^\circ \], and angle 10 is\[55{}^\circ \].
Work Step by Step
Compute the measurement of angle 1 using the fact that vertically opposite angles are equal to each other. Thus, \[m\measuredangle 1=55{}^\circ \].
Compute angle 7 using the fact that angles whose measurement is \[120{}^\circ \] and angle 7 forms a straight angle. Therefore, their sum is equal to \[180{}^\circ \].
\[\angle 7+120{}^\circ =180{}^\circ \]
Compute the measurement of angle 7 by subtracting \[120{}^\circ \]from both the sides of equation.
\[\begin{align}
& \angle 7=180{}^\circ -120{}^\circ \\
& \angle 7=60{}^\circ \\
\end{align}\]
Compute the measurement of angle 8 using the fact that vertically opposite angles are equal to each other: m\[\measuredangle 8=\text{m}\measuredangle 7\]. Thus, \[m\angle 8=60{}^\circ \].
Compute the measurement of angle 6 using the fact that vertically opposite angles are equal to each other. Thus, \[m\measuredangle 6=120{}^\circ \].
Compute the measurement of angle 5 using the fact that alternate angles are equal to each other: \[m\measuredangle 5=m\measuredangle 7\]. Thus, \[\angle 5=60{}^\circ \].
Compute angle 4 using the fact that angles\[55{}^\circ \], angle 4, and angle 5 forms a straight angle. Therefore, their sum is equal to\[180{}^\circ \].
Sum of all the three angels of a triangle is \[180{}^\circ \].
\[\begin{align}
& 55{}^\circ +\measuredangle 4+\measuredangle 5=180{}^\circ \\
& 55{}^\circ +\measuredangle 4+60{}^\circ =180{}^\circ \\
& \measuredangle 4=180{}^\circ -115{}^\circ \\
& \measuredangle 4=65{}^\circ
\end{align}\]
Compute the measurement of angle 2 using the fact that vertically opposite angles are equal to each other: \[m\measuredangle 2=m\measuredangle 4\]. Thus, \[m\measuredangle 2=65{}^\circ \].
Compute the measurement of angle 3 using the fact that vertically opposite angles are equal to each other: \[m\measuredangle 3=m\measuredangle 5\]. Thus, \[m\measuredangle 3=60{}^\circ \].
Compute the measurement of angle 9 using the fact that alternate angles are equal to each other. Thus, \[m\measuredangle 9=55{}^\circ \].
Compute the measurement of angle 10 using the fact that vertically opposite angles are equal to each other: \[m\measuredangle 10=m\measuredangle 9\]. Thus, \[m\measuredangle 10={{55}^{\circ }}\].
Hence, the measurement of angle 1 is \[{{55}^{{}^\circ }}{}^\circ \], angle 2 is \[65{}^\circ \], angle 3 is \[60{}^\circ \], angle 4 is \[65{}^\circ \], angle 5 is\[60{}^\circ \], angle 6 is\[120{}^\circ \], angle 7 is \[60{}^\circ \], angle 8 is\[60{}^\circ \], angle 9 is\[55{}^\circ \], and angle 10 is\[55{}^\circ \].
