what is $m\\angle stu$?\nwrite your answer as an integer or decimal.\n$m\\angle stu = \\square^{\\circ}$
what is $m\\angle stu$?\nwrite your answer as an integer or decimal.\n$m\\angle stu = \\square^{\\circ}$
Answer
Explanation:
Step1: Identify the triangle type
The segments $RU$ and $RT$ are radii of the circle, so $RU = RT$. Thus, $\triangle RUT$ is an isosceles triangle.
Step2: Use the triangle sum theorem
The sum of the interior angles of a triangle is $180^{\circ}$. In an isosceles triangle, the base angles are equal. $$m\angle RUT + m\angle RTU + m\angle URT = 180^{\circ}$$
Step3: Substitute known values and solve
Since $m\angle RUT = m\angle RTU$ and $m\angle URT = 78^{\circ}$: $$2 \cdot m\angle RTU + 78^{\circ} = 180^{\circ}$$
Step4: Calculate the final angle
$$2 \cdot m\angle RTU = 180^{\circ} - 78^{\circ} = 102^{\circ}$$ $$m\angle RTU = \frac{102^{\circ}}{2} = 51^{\circ}$$
Answer:
51