Question

find the measure of each marked angle. the degree measure of the top angle of the triangle, with angle measure (6x - 110)°, is 70°. the degree measure of the bottom left angle of the triangle, with angle measure (x + 30)°, is 60°. the angle with measure (6x - 50)°, that is supplement to the last interior angle of the triangle is ☐°.

Explanation:

Step1: Find the value of x from the bottom left angle

We know the bottom left angle is \((x + 30)^\circ=60^\circ\) (wait, the problem says \((x - 30)^\circ\)? Wait, the problem statement has a typo? Wait, the user's problem: "The degree measure of the bottom left angle of the triangle, with angle measure \((x + 30)^\circ\), is \(60^\circ\)". Wait, original diagram: \((x - 30)^\circ\)? Wait, maybe the user made a typo, but let's go with the given: \((x + 30)^\circ = 60^\circ\). So solve for x:
\(x+30 = 60\)
\(x=60 - 30=30\)? Wait, no, wait the top angle is \((6x - 110)^\circ = 70^\circ\). Let's check with top angle: \(6x-110 = 70\)
\(6x=70 + 110=180\)
\(x = 30\). Ah, so x is 30. Then the bottom left angle: if the diagram is \((x - 30)^\circ\), then \(30 - 30 = 0\), which is wrong. So probably the bottom left angle is \((x + 30)^\circ\), and x=30, so \(30 + 30 = 60\), which matches. So x=30.

Step2: Calculate the angle \((6x - 50)^\circ\)

Now, substitute x = 30 into \((6x - 50)^\circ\):
\(6\times30 - 50=180 - 50 = 130\)

Answer:

\(130\)