Question

a triangle with two equal - length sides (marked by two short cross - lines on the sides). the two base angles are marked as ((5x + 9)^{circ}) and ((8x - 30)^{circ}) respectively.

Explanation:

Step1: Identify equal base angles

The triangle has two equal sides, so its base angles are equal:
$5x + 9 = 8x - 30$

Step2: Rearrange to solve for x

Subtract $5x$ and add 30 to both sides:
$9 + 30 = 8x - 5x$
$39 = 3x$
$x = \frac{39}{3}$

Step3: Calculate the value of x

Simplify the division:
$x = 13$

Answer:

$x = 13$