Question

what are the values of s and t?
(there is a triangle hgi with angle at h being 58 degrees, and two sides (hg and gi) marked as equal with red ticks. angle at i is s degrees, angle at g is t degrees. then s = °, t = °)

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle HGI \) has two sides marked as equal (the red ticks), so it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. The side opposite angle \( H \) (which is \( 58^\circ \)) is \( GI \), and the side opposite angle \( I \) (which is \( s \)) is \( HG \). Since \( HG = GI \) (marked equal), their opposite angles are equal. So \( s = 58^\circ \).

Step2: Calculate angle \( t \)

The sum of the interior angles of a triangle is \( 180^\circ \). So we have \( \angle H + \angle I + \angle G = 180^\circ \). We know \( \angle H = 58^\circ \) and \( \angle I = s = 58^\circ \). Substituting these values: \( 58^\circ + 58^\circ + t = 180^\circ \).
First, add \( 58^\circ \) and \( 58^\circ \): \( 58 + 58 = 116 \). So \( 116^\circ + t = 180^\circ \).
Then, solve for \( t \): \( t = 180^\circ - 116^\circ = 64^\circ \).

Answer:

\( s = 58^\circ \)
\( t = 64^\circ \)