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\(\textbf{1)}\) Solve for x.

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The answer is \(x=2\)

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\(\,\,\,\,\,\,\text{The legs in an isosceles triangle are congruent.}\)

\(\,\,\,\,\,\,3x+5=5x+1\)

\(\,\,\,\,\,\,5=2x+1\)

\(\,\,\,\,\,\,4=2x\)

\(\,\,\,\,\,\,\)The answer is \(x=2\)

\(\textbf{2)}\) Solve for x.

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The answer is \(x=60\)

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\(\,\,\,\,\,\,\text{The base angles in an isosceles triangle are congruent.}\)

\(\,\,\,\,\,\,x-10=50\)

\(\,\,\,\,\,\,\)The answer is \(x=60\)

\(\textbf{3)}\) Solve for x.

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The answer is \(x=65\)

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\(\,\,\,\,\,\,\text{The base angles in an isosceles triangle are congruent.}\)

\(\,\,\,\,\,\,x+x+50=180\)

\(\,\,\,\,\,\,2x=130\)

\(\,\,\,\,\,\,\)The answer is \(x=65\)

\(\textbf{4)}\) Solve for x.

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The answer is \(x=40\)

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\(\,\,\,\,\,\,\text{The base angles in an isosceles triangle are congruent.}\)

\(\,\,\,\,\,\,x+70+70=180\)

\(\,\,\,\,\,\,x+140=180\)

\(\,\,\,\,\,\,\)The answer is \(x=40\)

\(\textbf{5)}\) Solve for x and y.

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The answer is \(x=8, y=50\)

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\(\,\,\,\,\,\,\text{The base angles in an isosceles triangle are congruent.}\)

\(\,\,\,\,\,\,2\text{(Base Angle)}+96=180\)

\(\,\,\,\,\,\,2\text{(Base Angle)}=84\)

\(\,\,\,\,\,\,\text{(Base Angle)}=42\)

\(\,\,\,\,\,\,\text{(Base Angle)}=5x+2=42\)

\(\,\,\,\,\,\,5x=40\)

\(\,\,\,\,\,\,x=8\)

\(\,\,\,\,\,\,\text{(Base Angle)}=y-8=42\)

\(\,\,\,\,\,\,y=50\)

\(\,\,\,\,\,\,\)The answer is \(x=8, y=50\)

\(\textbf{6)}\) Solve for x and y.

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The answer is \(x=52, y=32\)

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\(\,\,\,\,\,\,\text{The base angles in an isosceles triangle are congruent.}\)

\(\,\,\,\,\,\,y+32=2y\)

\(\,\,\,\,\,\,32=y\)

\(\,\,\,\,\,\,\left(6y+32\right)+\left(2y\right)=180\)

\(\,\,\,\,\,\,\left(64\right)+\left(64\right)+x=180\)

\(\,\,\,\,\,\,128+x=180\)

\(\,\,\,\,\,\,x=52\)

\(\,\,\,\,\,\,\)The answer is \(x=52, y=32\)

\(\textbf{7)}\) This is an isosceles triangle. What are the possible values of x?

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The answer is \(x=69\)

See Related Pages\(\)

\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Triangle Angle Sum Theorem}\)
\(\,\,\,\,\,\,\,\,\angle A+ \angle B+ \angle C=180^{\circ}…\)

\(\bullet\text{ Exterior Angle Theorem}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Side Splitter Theorem}\)
\(\,\,\,\,\,\,\,\,\)

\(\bullet\text{ Area and Perimeter of Triangles}\)
\(\,\,\,\,\,\,\,\,\)\(\,\, A=\frac{1}{2}bh, \,\, P=s_1+s_2+s_3…\)

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