The measure of each angle is 117°
Explanation:
Given that the two angles are (11x-26)° and (7x+26)°
We need to determine the measure of each angle.
Measure of angles:
From the figure, it is obvious that the two angles are vertically opposite angles.
By definition, we know that, the vertically opposite angles are always equal.
To determine the measure of each angle, we shall first find the value of x.
Thus, we have,
[tex]11x-26=7x+26[/tex]
[tex]4x-26=26[/tex]
[tex]4x=52[/tex]
[tex]x=13[/tex]
Thus, the value of x is 13
Now, substituting [tex]x=13[/tex] in the angle (11x-26)°, we get,
[tex](11(13)-26)^{\circ}=(143-26)^{\circ}[/tex]
[tex]=117^{\circ}[/tex]
The measure of the angle is 117°
Similarly, substituting [tex]x=13[/tex] in the angle (7x+26)°, we get,
[tex](7x+26)^{\circ}=(7(13)+26)^{\circ}[/tex]
[tex]=117^{\circ}[/tex]
The measure of the angle is 117°
Hence, the measure of each angle is 117°
