We want to find the measure of x given that we know that m and n are congruent.
The measure of x is 116°.
Two angles are congruent if they have the same measure.
Then we have ∠n = ∠m
We also know that the sum of all interior angles of a triangle is equal to 180°, then if we look at the smaller triangle we have that:
114° + ∠n + ∠m = 180°
∠n + ∠m = 180° - 114° = 66°
Knowing that these measures are equal we can write:
2*∠m = 66°
∠m = 66°/2 = 33°
Now that we know the measure of m, we can do the same thing for the larger triangle:
∠x + ∠m + 31° = 180°
∠x + 33° + 31° = 180°
∠x = 180° - 64° = 116°
The measure of x is 116°.
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Applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: [tex]\mathbf{x = 64^{\circ}}[/tex]
Recall:
Sum of triangles = 180 degrees
Exterior angle = sum of two interior opposite angles
Since we know that angles m and n are congruent, therefore:
[tex]m = \frac{1}{2} (180 - m \angle RTU)[/tex]
[tex]m = \frac{1}{2} (180 - 114)\\\\\mathbf{m = 33^{\circ}}[/tex]
Find x (exterior angle of triangle SUV):
[tex]x = 31 + m[/tex] (exterior angle of a triangle theorem)
[tex]x = 31 + 33\\\\\mathbf{x = 64^{\circ}}[/tex]
Therefore, applying the exterior angle theorem and the sum of triangles, the value of x in the figure is: [tex]\mathbf{x = 64^{\circ}}[/tex]
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