Question

find all the measure of the missing angles in the triangle below. a 3x - 6 130° 8x + 4 30 100 40 90

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $(3x - 6)+(8x + 4)=130$.

Step2: Simplify the left - hand side

Combine like terms: $3x+8x-6 + 4=130$, which gives $11x-2 = 130$.

Step3: Solve for x

Add 2 to both sides: $11x=130 + 2=132$. Then divide both sides by 11: $x=\frac{132}{11}=12$.

Step4: Find the first interior angle

Substitute $x = 12$ into $3x-6$: $3\times12-6=36 - 6=30$.

Step5: Find the second interior angle

Substitute $x = 12$ into $8x + 4$: $8\times12+4=96 + 4=100$.

Step6: Find the third interior angle

The sum of the interior angles of a triangle is $180^{\circ}$. Let the third angle be $y$. Then $30+100+y = 180$. So, $y=180-(30 + 100)=50$. But we are asked for the non - supplementary angles related to the given expressions.

Answer:

30, 100