QuestionAugust 25, 2025

angle 1 and angle 2 form a llnear pair.If mangle 1=6x+1 and mangle 2=2x-5 . find the measures of both angles.

angle 1 and angle 2 form a llnear pair.If mangle 1=6x+1 and mangle 2=2x-5 . find the measures of both angles.
angle 1 and angle 2 form a llnear pair.If mangle 1=6x+1 and mangle 2=2x-5 . find the measures of both angles.

Solution
4.6(90 votes)

Answer

m\angle 1 = 139^\circ, m\angle 2 = 41^\circ Explanation 1. Set up the equation for a linear pair A linear pair of angles sums to 180^\circ. Therefore, m\angle 1 + m\angle 2 = 180. 2. Substitute expressions for angles Substitute 6x + 1 for m\angle 1 and 2x - 5 for m\angle 2: (6x + 1) + (2x - 5) = 180. 3. Simplify and solve for x Combine like terms: 8x - 4 = 180. Add 4 to both sides: 8x = 184. Divide by 8: x = 23. 4. Calculate m\angle 1 Substitute x = 23 into m\angle 1 = 6x + 1: m\angle 1 = 6(23) + 1 = 139. 5. Calculate m\angle 2 Substitute x = 23 into m\angle 2 = 2x - 5: m\angle 2 = 2(23) - 5 = 41.

Explanation

1. Set up the equation for a linear pair<br /> A linear pair of angles sums to $180^\circ$. Therefore, $m\angle 1 + m\angle 2 = 180$.<br />2. Substitute expressions for angles<br /> Substitute $6x + 1$ for $m\angle 1$ and $2x - 5$ for $m\angle 2$: $(6x + 1) + (2x - 5) = 180$.<br />3. Simplify and solve for $x$<br /> Combine like terms: $8x - 4 = 180$. Add 4 to both sides: $8x = 184$. Divide by 8: $x = 23$.<br />4. Calculate $m\angle 1$<br /> Substitute $x = 23$ into $m\angle 1 = 6x + 1$: $m\angle 1 = 6(23) + 1 = 139$.<br />5. Calculate $m\angle 2$<br /> Substitute $x = 23$ into $m\angle 2 = 2x - 5$: $m\angle 2 = 2(23) - 5 = 41$.
Click to rate:

Similar Questions