Question

use the given information to find m∠a. m∠d = 119°, m∠a=(2x)°, m∠b=(x + 30.5)°. (the figure is not drawn to scale)

Explanation:

Step1: Use angle - sum property (assuming a relevant geometric relationship)

Since we assume that \(\angle A+\angle B = \angle D\) (a common geometric relationship for adjacent - angles or angles formed by intersecting lines). Substitute the given angle expressions: \(2x+(x + 30.5)=119\).

Step2: Combine like - terms

Combine the \(x\) terms on the left - hand side: \(2x+x+30.5 = 119\), which simplifies to \(3x+30.5 = 119\).

Step3: Isolate the variable term

Subtract 30.5 from both sides of the equation: \(3x=119 - 30.5\), so \(3x=88.5\).

Step4: Solve for \(x\)

Divide both sides by 3: \(x=\frac{88.5}{3}=29.5\).

Step5: Find \(m\angle A\)

Since \(m\angle A=(2x)^{\circ}\), substitute \(x = 29.5\) into the expression for \(m\angle A\). Then \(m\angle A=2\times29.5^{\circ}=59^{\circ}\).

Answer:

\(59\)