Question

what are the values of b and c?
(there is a triangle hgi with angle at h being 55 degrees, and two sides marked as equal, angle at i is b degrees, angle at g is c degrees, and the base gi is marked as equal to one of the other sides. then b = \square^\circ, c = \square^\circ)

Explanation:

Step1: Identify triangle type

The triangle has two equal sides (marked with ticks), so it's isosceles. Thus, \( b = c \).

Step2: Use triangle angle sum

Triangle angle sum is \( 180^\circ \). Let \( b = c = x \). So, \( 55^\circ + x + x = 180^\circ \).

Step3: Solve for x

Simplify: \( 55 + 2x = 180 \). Subtract 55: \( 2x = 180 - 55 = 125 \). Divide by 2: \( x = \frac{125}{2} = 62.5 \).

Answer:

\( b = 62.5^\circ \), \( c = 62.5^\circ \)