Question

geometry
name lice doyola id: 1
angle pair relationships with equations date 12/9/25 period 5
find the value of x.
1)
2)
3)
4)
5)
6)

Explanation:

Problem 1:

Step 1: Identify Angle Relationship

The angles \(5x^\circ\), \((3x + 2)^\circ\) form a right angle (since there's a right - angle symbol), so their sum is \(90^\circ\). So the equation is \(5x+(3x + 2)=90\).

Step 2: Solve the Equation

Combine like terms: \(5x+3x + 2=90\) gives \(8x+2 = 90\). Subtract 2 from both sides: \(8x=90 - 2=88\). Divide both sides by 8: \(x=\frac{88}{8} = 11\).

Problem 2:

Step 1: Identify Angle Relationship

The angles \((2x + 1)^\circ\) and \((x-55)^\circ\) are supplementary (they form a straight line), so their sum is \(180^\circ\). The equation is \((2x + 1)+(x - 55)=180\).

Step 2: Solve the Equation

Combine like terms: \(2x+1+x - 55=180\) gives \(3x-54 = 180\). Add 54 to both sides: \(3x=180 + 54=234\). Divide both sides by 3: \(x = 78\).

Problem 3:

Step 1: Identify Angle Relationship

The angles \((4x + 2)^\circ\) and \(58^\circ\) are vertical angles? No, wait, they are supplementary? Wait, no, if two lines intersect, vertical angles are equal. Wait, looking at the diagram, \((4x + 2)^\circ\) and \(58^\circ\) are vertical angles? Wait, no, actually, if we consider the straight line, but in the diagram, the two angles \((4x + 2)^\circ\) and \(58^\circ\) are equal (vertical angles). So \(4x+2 = 58\).

Step 2: Solve the Equation

Subtract 2 from both sides: \(4x=58 - 2 = 56\). Divide both sides by 4: \(x=\frac{56}{4}=14\).

Problem 4:

Answer:

s:

1. \(x = 11\)
2. \(x = 78\)
3. \(x = 14\)
4. \(x = 14\)
5. \(x = 16\)
6. \(x = 33\)