Based on the triangle sum theorem, the measure of angle x include; D. 23°.
In Mathematics and Geometry, a supplementary angle refers to two angles or arc whose sum is equal to 180 degrees.
According to the triangle sum theorem, the sum of the angles in a triangle is equal to 180°. Therefore, we have these supplementary angles:
m∠A + m∠B + m∠C = 180°
Note: The 110 degrees angle would move down into the triangle based on the vertical angles theorem.
By using the substitution property, we have the following;
110° + 57° + x = 180°
x = 180° - (100 + 57)°
m∠1 = 180° - 157
m∠1 = 23°