Question

solve for x.
17)
18)
find the measure of angle a.
19)
20)

Explanation:

Step1: Use the triangle - angle - sum theorem

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

For problem 17:

Step1: Set up the equation

\((x + 70)+76 + 41=180\)

Step2: Simplify the left - hand side

\(x+70+117 = 180\), so \(x + 187=180\)

Step3: Solve for \(x\)

Subtract 187 from both sides: \(x=180 - 187=-7\)

For problem 18:

Step1: Use the right - triangle angle - sum

In a right - triangle (\(90^{\circ}\) angle), \(25+(x + 69)+90=180\)

Step2: Simplify the left - hand side

\(x+25+69 + 90=x + 184\)

Step3: Solve for \(x\)

\(x+184 = 180\), so \(x=180-184=-4\)

For problem 19:

Step1: Apply the triangle - angle - sum theorem

\((57 + x)+(x + 87)+50=180\)

Step2: Combine like terms

\(2x+57+87 + 50=2x+194\)

Step3: Solve for \(x\)

\(2x+194 = 180\), \(2x=180 - 194=-14\), \(x=-7\)

Step4: Find angle \(A\)

Angle \(A=57+x\), substitute \(x = - 7\), \(A=57-7 = 50^{\circ}\)

For problem 20:

Step1: Use the triangle - angle - sum theorem

\((9x + 4)+(16x-4)+80=180\)

Step2: Combine like terms

\(25x+80=180\)

Step3: Solve for \(x\)

\(25x=180 - 80 = 100\), \(x = 4\)

Step4: Find angle \(A\)

Angle \(A=9x + 4\), substitute \(x = 4\), \(A=9\times4+4=40^{\circ}\)

Answer:

1. \(x=-7\)
2. \(x=-4\)
3. \(\angle A = 50^{\circ}\)
4. \(\angle A = 40^{\circ}\)