Question

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

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). In a right - triangle, one angle is \(90^{\circ}\), and the other two angles are \((3x - 3)^{\circ}\) and \((4x - 5)^{\circ}\). So, we can write the equation: \((3x - 3)+(4x - 5)+90=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x-3 + 4x-5+90=(3x + 4x)+(-3-5 + 90)=7x+82\). The equation becomes \(7x + 82=180\).

Step3: Solve for \(x\)

Subtract \(82\) from both sides: \(7x+82 - 82=180 - 82\), which gives \(7x=98\). Then divide both sides by \(7\): \(x=\frac{98}{7}=14\).

Answer:

\(x = 10\)