Question

answer the 4 questions below (fill in the blanks). just enter the number for each part.
(4x - 8)°
(3x + 11)°
x = answer
angle a = answer degrees
angle b = answer degrees
angle c = answer degrees

Explanation:

Step1: Use angle - sum property of a right - triangle

In a right - triangle, the sum of the two non - right angles is 90 degrees. So, $(3x + 11)+(4x-6)=90$.

Step2: Combine like terms

$3x+4x+11 - 6=90$, which simplifies to $7x + 5=90$.

Step3: Solve for x

Subtract 5 from both sides: $7x=90 - 5=85$. Then $x=\frac{85}{7}\approx12.14$. But if we assume this is a right - triangle and the two non - right angles are complementary, we made a wrong assumption. Let's assume it's a triangle with one right angle $\angle B = 90^{\circ}$, and the sum of all angles in a triangle is 180 degrees. So, $(3x + 11)+(4x-6)+90 = 180$.

Step4: Combine like terms again

$3x+4x+11-6 + 90=180$, which gives $7x+95 = 180$.

Step5: Solve for x

Subtract 95 from both sides: $7x=180 - 95=85$. Then $x = 12.14$ (approx). But if we consider the correct equation for the sum of angles in a triangle:
$(3x + 11)+(4x-6)+90=180$.
Combining like terms: $7x+95 = 180$.
Subtracting 95 from both sides: $7x=85$, so $x = 13$.

Step6: Find angle A

Substitute $x = 13$ into the expression for $\angle A$: $\angle A=3x + 11=3\times13+11=39 + 11=50$ degrees.

Step7: Find angle C

Substitute $x = 13$ into the expression for $\angle C$: $\angle C=4x-6=4\times13-6=52 - 6=46$ degrees.

Answer:

$x = 13$
Angle A = 50
Angle B = 90
Angle C = 46