Questions: Suppose that triangle GHI is isosceles with base IG. Suppose also that m angle H=(3x+19)° and m angle I=(4x-2)°. Find the degree measure of each angle in the triangle.

Suppose that triangle GHI is isosceles with base IG. Suppose also that m angle H=(3x+19)° and m angle I=(4x-2)°. Find the degree measure of each angle in the triangle.

Transcript text: Suppose that $\triangle G H I$ is isosceles with base $\overline{I G}$. Suppose also that $m \angle H=(3 x+19)^{\circ}$ and $m \angle I=(4 x-2)^{\circ}$. Find the degree measure of each angle in the triangle.

Solution

Solution Steps

Step 1: Set up the equation

Since triangle _GHI_ is an isosceles triangle with base _IG_, angles _I_ and _G_ are congruent. Therefore, we know that _m∠I = m∠G_. Since the sum of the interior angles of a triangle is equal to 180°, we can set up the following equation:

_m∠I + m∠G + m∠H = 180°_.

Substituting the given values and _m∠I_ for _m∠G_, we get

_(4x - 2)° + (4x - 2)° + (3x + 19)° = 180°_.

Step 2: Solve for x

Simplifying the equation, we get

_11x + 15 = 180_.

Subtract 15 from both sides:

_11x = 165_.

Divide both sides by 11:

_x = 15_.

Step 3: Calculate the angles

Substitute _x = 15_ into the expressions for each angle: