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 \\(\square\\)°. (diagram shows a triangle with angles: top \\((6x - 110)°\\), bottom left \\((x + 30)°\\), bottom right exterior \\((6x - 50)°\\), and a straight line at the base.)

Explanation:

Step1: Find x using top angle

We know the top angle is \( (6x - 110)^\circ = 70^\circ \). Solve for \( x \):
\( 6x - 110 = 70 \)
\( 6x = 70 + 110 \)
\( 6x = 180 \)
\( x = \frac{180}{6} = 30 \)

Step2: Calculate bottom left angle

Now, substitute \( x = 30 \) into \( (x + 30)^\circ \):
\( (30 + 30)^\circ = 60^\circ \)

Answer:

\( 60 \)