Let us first solve the triangle on the right side involving angle x.
Recall that the sum of angles in a triangle must be equal to 180°.
So we can write
[tex]\begin{gathered} 41+78+x=180 \\ 119+x=180 \\ x=180-119 \\ x=61\degree \end{gathered}[/tex]Therefore, the angle x is equal to 61°
Now let us solve the triangle involving angle S and T.
Again applying the property that the sum of angles in a triangle must be equal to 180°
[tex]\begin{gathered} 48+57+S=180 \\ 105+S=180 \\ S=180-105 \\ S=75\degree \end{gathered}[/tex]As you can see, the angle S and T form a straight line angle.
Recall that a straight line angle is equal to 180°
[tex]\begin{gathered} S+T=180 \\ 75+T=180 \\ T=180-75 \\ T=105\degree \end{gathered}[/tex]Therefore, angle S = 75° and angle T = 105°
Now let us solve the remaining figure.
On the right side of the figure, apply the property that the sum of angles in a triangle must be equal to 180°
[tex]\begin{gathered} A+42+40=180 \\ A+82=180 \\ A=180-82 \\ A=98\degree \end{gathered}[/tex]As you can see, the angles A and B are opposite angles.
We know that opposite angles are equal.
[tex]\angle A=\angle B=98\degree[/tex]Now we know the angle B so let us apply the property that the sum of angles in a triangle must be equal to 180°
[tex]\begin{gathered} B+48+C=180 \\ 98+48+C=180 \\ 146+C=180 \\ C=180-146 \\ C=34\degree \end{gathered}[/tex]Therefore, angle A = 98° and angle B = 98° and angle C = 34°
