Question

If mDH =(11x + 7) degrees , mGF = (5x + 9) degrees , and mEF = (10x - 22) degrees, find mDH

Answer 1

For this problem we use the arcs and chords theorem we know that

`\begin{gathered} \measuredangle H\text{EF=}(1)/(2)(mGF+mDH) \\ \text{Substituting }\measuredangle HEF=10x-22,\text{ mGF=5x+9 and mDH=11x+7 we get} \\ 10x-22=(1)/(2)(5x+9+11x+7) \end{gathered}`

Solving for x we get:

`\begin{gathered} 10x-22=(1)/(2)(16x+16)=8x+8 \\ 2x=30 \\ x=15 \end{gathered}`

Finally, we substitute x for mDH=(11x+7) degrees=(11*15+7) degrees=172 degrees.

mDH=172 degrees.