Question

use the diagram to the right to answer #18 - 21. 18. x = __________ 19. m∠a = ____ 20. m∠b = ____ 21. m∠c = ______

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, $(6x + 12)+(5x - 3)+(5x+3)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $6x+5x + 5x+12-3 + 3=180$, which gives $16x+12 = 180$.

Step3: Solve for x

Subtract 12 from both sides: $16x=180 - 12=168$. Then divide both sides by 16: $x=\frac{168}{16}=\frac{42}{4} = 10.5$.

Step4: Find $m\angle A$

Substitute $x = 10.5$ into the expression for $\angle A$: $m\angle A=6x + 12=6\times10.5+12=63 + 12=75^{\circ}$.

Step5: Find $m\angle B$

Substitute $x = 10.5$ into the expression for $\angle B$: $m\angle B=5x - 3=5\times10.5-3=52.5-3 = 49.5^{\circ}$.

Step6: Find $m\angle C$

Substitute $x = 10.5$ into the expression for $\angle C$: $m\angle C=5x + 3=5\times10.5+3=52.5+3=55.5^{\circ}$.

Answer:

1. $x = 10.5$
2. $m\angle A=75^{\circ}$
3. $m\angle B = 49.5^{\circ}$
4. $m\angle C=55.5^{\circ}$