M midpoint of DE, m<1>m<2DF=13x-5, Ef=7x+25, find x

[rubyred]

If M is the midpoint of segment DE m<1>m<2DF=13x-5 and Ef =7x +25 find alll possible values of x.

 

[rubyred]

Re: Hard geometry question

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[rubyred]

Re: Hard geometry question

THat's the picture that goes along with this equation how would i solve it because i can't solve it and put there equal and i can't put they equal 180 please help!

 

[Mrspi]

If M is the midpoint of segment DE m<1>m<2DF=13x-5 and Ef =7x +25 find alll possible values of x.

If M is the midpoint of DE, then DM = ME.

MF = MF

<1 > <2

In triangles MEF and MDF, you have two pairs of equal sides, but the angles included between those sides are UNEQUAL. You should have a theorem that says "If two triangles have a pair of equal sides, but the included angles are unequal, then the sides opposite the unequal angles are also unequal in the same order."

Since <1 > <2, the side of triangle MDF which is opposite <1 must be greater than the side of triangle MEF which is opposite <2.

Or,

DF > EF

Now....you are GIVEN expressions for the lengths DF and EF. Substitute those expressions in the above inequality, and solve for the possible values of x.