Question

1. the ( mangle u = 3x^circ ), and ( mangle v = 2(mangle u)^circ ). find the value of ( x ) that makes ( angle u ) and ( angle v ) supplementary angles.

( x = 20 )

Explanation:

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\). So \(m\angle U + m\angle V = 180^\circ\).

Step2: Substitute \(m\angle V\)

Given \(m\angle V = 2(m\angle U)\), and \(m\angle U = 3x^\circ\), so \(m\angle V = 2(3x)^\circ = 6x^\circ\).

Step3: Set up equation

\(3x + 6x = 180\). Combine like terms: \(9x = 180\).

Step4: Solve for \(x\)

Divide both sides by 9: \(x = \frac{180}{9} = 20\).

Answer:

\(x = 20\)