Question

question image. diagram shows a right triangle tsu with right angle at u. point s is on a line with e, forming a 150° angle at s (between e and the side st). a question mark indicates the measure of angle at t (∠t).

Explanation:

Step1: Find the adjacent angle to 150°

Since \( \angle E S T \) and the angle at \( S \) inside the triangle are supplementary (they form a linear pair), we calculate the interior angle at \( S \) as \( 180^\circ - 150^\circ = 30^\circ \).

Step2: Use the triangle angle sum property

In a right - triangle \( \triangle SUT \) (since \( \angle U = 90^\circ \)), the sum of the interior angles of a triangle is \( 180^\circ \). Let the unknown angle at \( T \) be \( x \). We know that one angle is \( 90^\circ \) and another is \( 30^\circ \). So, \( x+90^\circ + 30^\circ=180^\circ \).
Simplifying the equation: \( x + 120^\circ=180^\circ \), then \( x=180^\circ - 120^\circ = 60^\circ \).

Answer:

The measure of the unknown angle at \( T \) is \( 60^\circ \)