Question

in the diagram, (overleftrightarrow{tu}) and (overleftrightarrow{ef}) intersect at point (y). if (mangle uyf = 42\frac{1}{5}^circ), what is (mangle fyt) in degrees?

Explanation:

Step1: Identify the angle relationship

Angles \(\angle UYF\) and \(\angle FYT\) are supplementary, meaning their sum is \(180^\circ\) because they form a linear pair (they are adjacent and their non - common sides form a straight line). So we can use the formula \(m\angle FYT=180^\circ - m\angle UYF\).

Step2: Substitute the given angle measure

We know that \(m\angle UYF = 42\frac{1}{5}^\circ=\frac{42\times5 + 1}{5}^\circ=\frac{211}{5}^\circ = 42.2^\circ\).
Now, \(m\angle FYT=180^\circ-\ 42\frac{1}{5}^\circ\).
First, convert \(180^\circ\) to a fraction with denominator 5: \(180^\circ=\frac{180\times5}{5}^\circ=\frac{900}{5}^\circ\).
Then, \(\frac{900}{5}-\frac{211}{5}=\frac{900 - 211}{5}=\frac{689}{5}=137\frac{4}{5}^\circ\) (or \(137.8^\circ\)).

Answer:

\(137\frac{4}{5}\) (or \(137.8\))