Question

suppose that $delta ghi$ is isosceles with base $overline{gi}$.suppose also that $mangle g=(5x + 16)^circ$ and $mangle i=(2x + 40)^circ$.find the degree measure of each angle in the triangle.$mangle g=square^circLXB0mangle i=square^circ$

Explanation:

Step1: Set base angles equal

Since $\triangle GHI$ is isosceles with base $\overline{GI}$, $\angle G$ and $\angle I$ are congruent.
$$5x + 16 = 2x + 40$$

Step2: Solve for $x$

Subtract $2x$ and 16 from both sides.
$$5x - 2x = 40 - 16$$
$$3x = 24$$
$$x = \frac{24}{3} = 8$$

Step3: Calculate $m\angle G$ and $m\angle I$

Substitute $x=8$ into the angle expressions.
$$m\angle G = 5(8) + 16 = 40 + 16 = 56^\circ$$
$$m\angle I = 2(8) + 40 = 16 + 40 = 56^\circ$$

Step4: Calculate $m\angle H$

Use triangle angle sum ($180^\circ$ total).
$$m\angle H = 180 - 56 - 56 = 68^\circ$$

Answer:

$m\angle G = 56^\circ$
$m\angle H = 68^\circ$
$m\angle I = 56^\circ$