Question

1. ∠a and ∠b are complementary. solve for x and find m∠a and m∠b. m∠a = 5x + 8 = ____ m∠b = x + 4 = __ x = __ 18. ∠a and ∠b are supplementary. solve for x and find m∠a and m∠b. m∠a = 3x = __ m∠b = x + 8 = __ x = ____

Explanation:

Step1: Use complementary - angle property

Since $\angle A$ and $\angle B$ are complementary, $m\angle A + m\angle B=90^{\circ}$. So, $(5x + 8)+(x + 4)=90$.

Step2: Simplify the equation

Combine like - terms: $5x+x+8 + 4=90$, which gives $6x+12 = 90$.

Step3: Solve for x

Subtract 12 from both sides: $6x=90 - 12=78$. Then divide both sides by 6: $x=\frac{78}{6}=13$.

Step4: Find $m\angle A$

Substitute $x = 13$ into $m\angle A=5x + 8$, so $m\angle A=5\times13+8=65 + 8=73^{\circ}$.

Step5: Find $m\angle B$

Substitute $x = 13$ into $m\angle B=x + 4$, so $m\angle B=13 + 4=17^{\circ}$.

For question 18:

Step1: Use supplementary - angle property

Since $\angle A$ and $\angle B$ are supplementary, $m\angle A + m\angle B = 180^{\circ}$. So, $3x+(x + 8)=180$.

Step2: Simplify the equation

Combine like - terms: $3x+x+8=180$, which gives $4x+8 = 180$.

Step3: Solve for x

Subtract 8 from both sides: $4x=180 - 8 = 172$. Then divide both sides by 4: $x=\frac{172}{4}=43$.

Step4: Find $m\angle A$

Substitute $x = 43$ into $m\angle A=3x$, so $m\angle A=3\times43 = 129^{\circ}$.

Step5: Find $m\angle B$

Substitute $x = 43$ into $m\angle B=x + 8$, so $m\angle B=43+8 = 51^{\circ}$.

Answer:

For question 17:
$x = 13$
$m\angle A=73^{\circ}$
$m\angle B=17^{\circ}$

For question 18:
$x = 43$
$m\angle A=129^{\circ}$
$m\angle B=51^{\circ}$