Question

true or false-- the value of x is 7? (image of two triangles with side lengths 21, 36, x, 12)

Explanation:

Step1: Identify triangle angle sum

The sum of angles in a triangle is $180^\circ$.

Step2: Calculate the third angle

The third angle of the triangle with angles $21^\circ$ and $x^\circ$ is $180^\circ - 21^\circ - x^\circ = 159^\circ - x^\circ$.

Step3: Use vertical angles property

The vertical angle to $36^\circ$ is also $36^\circ$. The triangle with angles $36^\circ$ and $12^\circ$ has a third angle of $180^\circ - 36^\circ - 12^\circ = 132^\circ$.

Step4: Check supplementary angles

The angles $159^\circ - x^\circ$ and $132^\circ$ are supplementary (form a straight line), so $159^\circ - x^\circ + 132^\circ = 180^\circ$.

Step5: Solve for x

$291^\circ - x^\circ = 180^\circ \implies x = 291 - 180 = 111$.

Answer:

False