Question

the state highway commission is building a new road as shown in the diagram. if ( mangle y ) is 73, what is ( mangle x )? a 39 b 34 c 29 d 59

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up the equation

Let the three angles of the triangle be \(68^{\circ}\), \(73^{\circ}\), and \(x\). Then \(68 + 73+x=180\).

Step3: Solve for \(x\)

First, add \(68\) and \(73\): \(68 + 73=141\). Then the equation becomes \(141+x = 180\). Subtract \(141\) from both sides: \(x=180 - 141\). So \(x = 39\).

Answer:

A. 39