Question

1. ∠g and ∠h are complementary angles. if m∠g = 6x - 15 and m∠h = 3x + 6, find m∠h. 25. ∠1 and ∠2 are vertical angles. if m∠1 = 5x + 12 and m∠2 = 6x - 11, find m∠1.

Explanation:

Step1: Use complementary - angle property

Since $\angle G$ and $\angle H$ are complementary, $m\angle G + m\angle H=90^{\circ}$.
So, $(6x - 15)+(3x + 6)=90$.

Step2: Simplify the left - hand side

Combine like terms: $6x+3x-15 + 6=90$, which gives $9x-9 = 90$.

Step3: Solve for $x$

Add 9 to both sides: $9x=90 + 9=99$.
Divide both sides by 9: $x = 11$.

Step4: Find $m\angle H$

Substitute $x = 11$ into the expression for $m\angle H$: $m\angle H=3x + 6$.
$m\angle H=3\times11+6=33 + 6=39^{\circ}$.

for question 25:

Step1: Use vertical - angle property

Since $\angle1$ and $\angle2$ are vertical angles, $m\angle1=m\angle2$.
So, $5x + 12=6x-11$.

Step2: Solve for $x$

Subtract $5x$ from both sides: $12=x - 11$.
Add 11 to both sides: $x=12 + 11=23$.

Step3: Find $m\angle1$

Substitute $x = 23$ into the expression for $m\angle1$: $m\angle1=5x + 12$.
$m\angle1=5\times23+12=115 + 12=127^{\circ}$.

Answer:

$39^{\circ}$