Question

the measures of the angles of a triangle are shown in the figure below. solve for x. 47° 58° x° answer attempt 1 out of 2 x = submit answer

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, if the angles of the triangle are \(47^{\circ}\), \(58^{\circ}\), and \(x^{\circ}\), then the equation is \(47 + 58+x=180\).

Step2: Simplify the left - hand side of the equation

First, add \(47\) and \(58\): \(47 + 58=105\). The equation becomes \(105+x = 180\).

Step3: Solve for \(x\)

Subtract \(105\) from both sides of the equation. Using the subtraction property of equality \(x=180 - 105\).

Answer:

\(x = 75\)