Question

solve for x. find the missing angles. show all work!
1.
2.
3.
4.

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). For the first triangle (right - angled triangle), we have \((x + 4)+(3x-22)+90=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+3x)+(4 - 22)+90=180\), which is \(4x-18 + 90=180\), then \(4x+72=180\).

Step3: Solve for \(x\)

Subtract 72 from both sides: \(4x=180 - 72\), so \(4x=108\). Divide both sides by 4: \(x=\frac{108}{4}=27\).

Step4: Find the angles

Substitute \(x = 27\) into the angle expressions.
For the first non - right angle: \(x + 4=27+4 = 31^{\circ}\).
For the second non - right angle: \(3x-22=3\times27-22=81 - 22=59^{\circ}\).

Answer:

\(x = 27\), the angles are \(31^{\circ}\), \(59^{\circ}\) and \(90^{\circ}\)