Question

in the triangle below, suppose that $m\angle i=(4x - 2)\degree$, $m\angle j=(6x - 5)\degree$, and $m\angle k=x\degree$.
find the degree measure of each angle in the triangle.
$m\angle i=\square\degree$
$m\angle j=\square\degree$
$m\angle k=\square\degree$

Explanation:

Step1: Use triangle angle sum theorem

The sum of angles in a triangle is \(180^\circ\). So, \((4x - 2)+(6x - 5)+x = 180\).

Step2: Simplify the equation

Combine like terms: \(4x+6x+x-2 - 5=180\) → \(11x-7 = 180\).

Step3: Solve for x

Add 7 to both sides: \(11x=180 + 7=187\). Divide by 11: \(x=\frac{187}{11}=17\).

Step4: Find each angle

• \(m\angle I=(4x - 2)^\circ\). Substitute \(x = 17\): \(4(17)-2=68 - 2 = 66^\circ\).
• \(m\angle J=(6x - 5)^\circ\). Substitute \(x = 17\): \(6(17)-5=102 - 5 = 97^\circ\).
• \(m\angle K=x^\circ=17^\circ\).

Answer:

\(m\angle I = 66^\circ\)
\(m\angle J = 97^\circ\)
\(m\angle K = 17^\circ\)