Question

3 find the value of x and the unknown angle in the triangle. (6x + 13)° 41° 78° x = 132 degrees unknown angle = 48 degrees

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we set up the equation $(6x + 13)+78 + 41=180$.

Step2: Simplify the left - hand side of the equation

First, add the constant terms: $13+78 + 41=132$. The equation becomes $6x+132 = 180$.

Step3: Solve for x

Subtract 132 from both sides: $6x=180 - 132$, so $6x = 48$. Then divide both sides by 6: $x=\frac{48}{6}=8$.

Step4: Find the unknown angle

The unknown angle is $6x + 13$. Substitute $x = 8$ into it: $6\times8+13=48 + 13=61$.

Answer:

$x = 8$
Unknown Angle $=61$ degrees