Question

if δbts ≅ δghd, bs = 25, ts = 14, bt = 31, gd = 4x - 11, m∠s = 56°, m∠b = 21°, and m∠h = (7y + 5)°, find the values of x and y.
identify the correct equation to help solve for y.
4x - 11 = 25
4x - 11 = 14
7y + 5 = 56
7y + 5 = 21
7y + 5 = 103

Explanation:

Step1: Recall Congruent Triangles

In congruent triangles \( \triangle BTS \cong \triangle GHD \), corresponding angles are equal. So \( \angle S \) corresponds to \( \angle H \), but wait, we need to find the equation for \( y \). Wait, the angle \( \angle S = 56^\circ \), and \( \angle H=(7y + 5)^\circ \)? Wait, no, the problem says "identify the correct equation to help solve for \( y \)". Since \( \triangle BTS \cong \triangle GHD \), corresponding angles are equal. So \( \angle S \) and \( \angle H \)? Wait, no, the given is \( m\angle S = 56^\circ \) and \( \angle H=(7y + 5)^\circ \)? Wait, maybe \( \angle S \) corresponds to \( \angle H \), so \( 7y + 5 = 56 \)? Wait, let's check the angles. The triangle congruence, so corresponding angles: \( \angle S \) should equal \( \angle H \) if the correspondence is \( BTS \cong GHD \), so \( \angle S = \angle H \), so \( 7y + 5 = 56 \). So the equation is \( 7y + 5 = 56 \).

Step2: Verify the Equation

Looking at the options, the equation \( 7y + 5 = 56 \) is one of them. So that's the correct equation to solve for \( y \).

Answer:

\( 7y + 5 = 56 \)