Question

what is the value of t?
(there is a diagram with points f, h, g, i. from f, two segments with equal marks (indicating congruent segments) go to h and i, with right angles at h (to g) and i (to i? wait, the diagram shows fh perpendicular to hg (right angle), fi perpendicular to hi (right angle), and angles at h: t + 73° and 6t + 53°)
t = \boxed{\space}°
submit

Explanation:

Step1: Identify Angle Bisector

The two segments from \( F \) to the perpendiculars are equal (marked with red ticks), so \( FH \) bisects \( \angle GHI \). Thus, the two angles \( t + 73^\circ \) and \( 6t + 53^\circ \) are equal.

Step2: Set Up Equation

Set \( t + 73 = 6t + 53 \).

Step3: Solve for \( t \)

Subtract \( t \) from both sides: \( 73 = 5t + 53 \).
Subtract 53: \( 20 = 5t \).
Divide by 5: \( t = 4 \).

Answer:

\( 4 \)