Question

find the measure of each angle indica
11)
find the value of x.
12)

Explanation:

Problem 11 (Angle in Triangle)

Step1: Find angle at T

Since \( \angle F T U = 118^\circ \) and it's a linear pair with \( \angle U T V \), we use \( \angle U T V = 180^\circ - 118^\circ = 62^\circ \).

Step2: Find angle at V

In \( \triangle U T V \), sum of angles is \( 180^\circ \). Given \( \angle U = 60^\circ \) and \( \angle U T V = 62^\circ \), so \( \angle V = 180^\circ - 60^\circ - 62^\circ = 58^\circ \).

Step1: Set up equation

The two angles \( 61^\circ \) and \( (x + 14)^\circ \) add up to \( 90^\circ \) (complementary angles). So, \( 61 + (x + 14) = 90 \).

Step2: Solve for \( x \)

Simplify: \( x + 75 = 90 \). Subtract 75: \( x = 90 - 75 = 15 \).

Answer:

The measure of the unknown angle (at \( V \)) is \( 58^\circ \).

Problem 12 (Find \( x \))

Assuming the angles are complementary (since there's a right angle implied by the diagram's perpendicular lines):