Question

this triangle is equilateral. find the value of x. (10x - 20)° (8x - 4)° x = ?

Explanation:

Step1: Recall properties of equilateral triangles

In an equilateral triangle, all angles are equal, and each angle measures \( 60^\circ \). Also, since it's equilateral, it's also isosceles, so the two given angles should be equal (because the sides opposite them are equal, as indicated by the tick marks). So we set the two angle expressions equal: \( 10x - 20 = 8x - 4 \).

Step2: Solve the equation for \( x \)

Subtract \( 8x \) from both sides: \( 10x - 8x - 20 = 8x - 8x - 4 \), which simplifies to \( 2x - 20 = -4 \). Then add 20 to both sides: \( 2x - 20 + 20 = -4 + 20 \), so \( 2x = 16 \). Divide both sides by 2: \( \frac{2x}{2} = \frac{16}{2} \), giving \( x = 8 \). We can also verify by plugging back in: for \( 10x - 20 \), \( 10(8)-20 = 80 - 20 = 60^\circ \); for \( 8x - 4 \), \( 8(8)-4 = 64 - 4 = 60^\circ \), which matches the angle measure of an equilateral triangle.

Answer:

\( x = 8 \)