Question

given a⊥b, find m∠1 and m∠2. 12 pts
x=
m∠1=
m∠2=

Explanation:

Step1: Use the property of perpendicular lines

Since \(a\perp b\), the sum of \(7x + 8\) and \(4x-6\) is \(90^{\circ}\).
\((7x + 8)+(4x-6)=90\)

Step2: Solve the equation for \(x\)

Combine like - terms: \(7x+4x+8 - 6=90\), \(11x+2 = 90\).
Subtract 2 from both sides: \(11x=90 - 2=88\).
Divide both sides by 11: \(x=\frac{88}{11}=8\).

Step3: Find \(m\angle1\)

Substitute \(x = 8\) into \(4x-6\).
\(m\angle1=4x-6=4\times8-6=32 - 6=26^{\circ}\).

Step4: Use the property of vertical angles

\(\angle2\) and \(7x + 8\) are vertical angles.
Substitute \(x = 8\) into \(7x + 8\): \(7\times8+8=56 + 8=64^{\circ}\). So \(m\angle2 = 64^{\circ}\).

Answer:

\(x = 8\)
\(m\angle1=26^{\circ}\)
\(m\angle2=64^{\circ}\)