MathDB

\triangle PAT,

\angle P=36^{\circ},

\angle A=56^{\circ},

and

PA=10.

Points

U

and

G

lie on sides

\overline{TP}

and

\overline{TA},

respectively, so that

PU=AG=1.

Let

M

and

N

be the midpoints of segments

\overline{PA}

and

\overline{UG},

respectively. What is the degree measure of the acute angle formed by lines

MN

and

PA?

<span class='latex-bold'>(A) </span> 76 \qquad <span class='latex-bold'>(B) </span> 77 \qquad <span class='latex-bold'>(C) </span> 78 \qquad <span class='latex-bold'>(D) </span> 79 \qquad <span class='latex-bold'>(E) </span> 80

Problem Statement