Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Use triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(60^{\circ}+90^{\circ}+(7x - 12)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

First, add the known angles: \(60 + 90+(7x-12)=180\). Then \(150+(7x - 12)=180\). Using the distributive property \(a+(b - c)=a + b - c\), we get \(150+7x-12 = 180\). Combine like terms: \(7x+(150 - 12)=180\), so \(7x + 138=180\).

Step3: Isolate the term with \(x\)

Subtract \(138\) from both sides of the equation: \(7x+138 - 138=180 - 138\). This gives \(7x=42\).

Step4: Solve for \(x\)

Divide both sides by \(7\): \(\frac{7x}{7}=\frac{42}{7}\).

Answer:

\(x = 6\)