Question

plete the statements about the relationship between the two labeled angles. given: the labeled angles form a right angle. the two labeled angles are complementary angles. that means that their measures sum to 90°. use the relationship you determined to w view solution history try again are you getting ahead of yourself? you dont need to enter the result of multiplying yet. multiply both sides :multiply both sides by what? 6x( ) = 120( )

Explanation:

Step1: Identify the relationship

The two angles \((2x)^\circ\) and \((4x - 30)^\circ\) are complementary, so their sum is \(90^\circ\). So we set up the equation: \(2x+(4x - 30)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(2x + 4x-30=6x - 30\). So the equation becomes \(6x-30 = 90\).

Step3: Solve for \(x\)

To solve for \(x\), we first add 30 to both sides of the equation: \(6x-30 + 30=90 + 30\), which simplifies to \(6x=120\). Then we divide both sides by 6: \(x=\frac{120}{6}=20\).

Step4: Find the angle measures

For the angle \((2x)^\circ\), substitute \(x = 20\): \(2\times20=40^\circ\). For the angle \((4x - 30)^\circ\), substitute \(x = 20\): \(4\times20-30=80 - 30 = 50^\circ\).

Answer:

The value of \(x\) is \(20\), the measure of the angle \((2x)^\circ\) is \(40^\circ\) and the measure of the angle \((4x - 30)^\circ\) is \(50^\circ\).