Question

find the value of ( x ) in the triangle shown below.
( x = square^circ )
(the triangle has two sides of length 12, one side of length 10.4, one angle of ( 62^circ ), and the angle at the vertex between the two sides of length 12 is ( x^circ ))

Explanation:

Step1: Identify triangle type

This is an isosceles triangle with two sides of length 12, so the angles opposite these sides are equal. Let the unknown angle at the top right be $y^\circ$, so $y = 62^\circ$.

Step2: Sum of triangle angles

The sum of interior angles in a triangle is $180^\circ$. Set up the equation:
$$x + 62 + 62 = 180$$

Step3: Calculate $x$

Simplify and solve for $x$:
$$x = 180 - 62 - 62$$
$$x = 56$$

Answer:

$56$