Question

in the diagram below we have that $d\widehat{u}v = 58^{circ}$ and $t\widehat{u}c = 62^{circ}$. find: 1. $a\widehat{b}t=square^{circ}$ 2. $b\widehat{c}t=square^{circ}$ 3. $d\widehat{u}c=square^{circ}$

Explanation:

Step1: Identify corresponding - angles

Assume \(AE\parallel SV\). \(\angle ABT\) and \(\angle DUV\) are corresponding - angles. Since corresponding angles are equal when two parallel lines are cut by a transversal, \(\angle ABT=\angle DUV\).
\(\angle ABT = 58^{\circ}\)

Step2: Identify alternate - interior angles

\(\angle BCT\) and \(\angle TUC\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(\angle BCT=\angle TUC\).
\(\angle BCT = 62^{\circ}\)

Step3: Calculate \(\angle DUC\)

\(\angle DUC\) and \(\angle TUC\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So \(\angle DUC = 180^{\circ}-\angle TUC\).
\(\angle DUC=180 - 62=118^{\circ}\)

Answer:

1. \(58\)
2. \(62\)
3. \(118\)