Question

(c) problem 18: (first taught in lesson 43)
find x.
5x - 8
2x + 7
after you enter your answer press go.
x =

Explanation:

Step1: Apply angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$. So, $40^{\circ}+40^{\circ}+(5x - 8)+(2x + 7)=180^{\circ}$.

Step2: Simplify the left - hand side

Combine like terms: $80^{\circ}+5x-8 + 2x+7=180^{\circ}$, which simplifies to $80^{\circ}+7x - 1=180^{\circ}$, and further to $7x+79^{\circ}=180^{\circ}$.

Step3: Solve for x

Subtract $79^{\circ}$ from both sides: $7x=180^{\circ}-79^{\circ}=101^{\circ}- 2^{\circ}=101^{\circ}-2^{\circ}=91^{\circ}$. Then divide both sides by 7: $x=\frac{91}{7}=13$. There was a mistake above. Let's correct.

The correct approach: Since the two non - x angles are equal, the triangle is isosceles and the sides opposite the equal angles are equal. So, $5x - 8=2x+7$.

Step1: Isolate x terms

Subtract $2x$ from both sides: $5x-2x - 8=2x-2x + 7$, which gives $3x-8=7$.

Step2: Solve for x

Add 8 to both sides: $3x-8 + 8=7 + 8$, so $3x=15$. Divide both sides by 3: $x = 5$.

Answer:

$x = 5$