Question

wednesday 11/12 and thursday 11/13 - lines and angles of dilation
practice score: 4/7 answered: 4/7
question 5
if ( \triangle rst-\triangle uvw ), find ( m angle w )
note: figures are not to scale.
( m angle w=) submit question

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle RST\sim\triangle UVW\), corresponding angles are equal. So \(\angle R=\angle U = 46^{\circ}\), \(\angle S=\angle V=86^{\circ}\), and \(\angle T=\angle W\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle RST\), we have \(\angle R+\angle S+\angle T = 180^{\circ}\). Substitute \(\angle R = 46^{\circ}\) and \(\angle S=86^{\circ}\) into the formula: \(46^{\circ}+86^{\circ}+\angle T=180^{\circ}\).

Step3: Solve for \(\angle T\)

First, calculate \(46 + 86=132\). Then the equation becomes \(132^{\circ}+\angle T=180^{\circ}\). Subtract \(132^{\circ}\) from both sides: \(\angle T=180^{\circ}- 132^{\circ}=48^{\circ}\).

Answer:

\(48\)