Question

find the value of x.
4.
5.
6.
7.
8.
9.

Explanation:

Step1: Identify vertical - angle relationship

In problem 4, vertical angles are equal. So we set up the equation $x + 25=90$.

Step2: Solve for $x$

Subtract 25 from both sides of the equation: $x=90 - 25$.
$x = 65$.

Step3: Identify complementary - angle relationship in problem 5

The two non - right angles are complementary. So $51+(2x - 11)=90$.

Step4: Simplify the equation

First, combine like terms: $2x+51 - 11=90$, which gives $2x + 40=90$.

Step5: Solve for $x$

Subtract 40 from both sides: $2x=90 - 40=50$. Then divide both sides by 2, $x = 25$.

Step6: Identify angle - sum relationship in problem 6

The sum of the two angles is 90 degrees. So $2x+x=90$.

Step7: Simplify and solve for $x$

Combine like terms: $3x=90$. Divide both sides by 3, $x = 30$.

Step8: Identify vertical - angle relationship in problem 7

We have $x-15 = 90$.

Step9: Solve for $x$

Add 15 to both sides: $x=90 + 15=105$.

Step10: Identify vertical - angle relationship in problem 8

We set up the equation $3x+6=90$.

Step11: Solve for $x$

Subtract 6 from both sides: $3x=90 - 6=84$. Then divide both sides by 3, $x = 28$.

Step12: Identify angle - sum relationship in problem 9

The sum of the two non - right angles is 90 degrees. So $(x - 15)+(x + 5)=90$.

Step13: Simplify the equation

Combine like terms: $x-15+x + 5=90$, which gives $2x-10=90$.

Step14: Solve for $x$

Add 10 to both sides: $2x=90 + 10=100$. Then divide both sides by 2, $x = 50$.

Answer:

1. $x = 65$
2. $x = 25$
3. $x = 30$
4. $x = 105$
5. $x = 28$
6. $x = 50$