This is an isosceles triangle. The angles at the base are congruent (they have the same measures).
Look at the picture.
We know: The sum of the measures of angles in a triangle is equal 180°.
Therefore we have the equation:
[tex]2x-10+2x-10+3x+25=180[/tex] combine like terms
[tex](2x+2x+3x)+(-10-10+25)=180[/tex]
[tex]7x+5=180[/tex] subtract 5 from both sides
[tex]7x=175[/tex] divide both sides by 7
[tex]x=25[/tex]
[tex]m\angle A=2x-10\to m\angle A=2(25)-10=50-10=40\\\\m\angle C=m\angle A=40\\\\m\angle B=3x+25\to m\angle B=3(25)+25=75+25=100^o[/tex]
Answer: D. m∠C = 40
