lines m and n are parallel.\nfind the measure of $\\angle a$.\n$m\\angle a = ? ^{\\circ}$

lines m and n are parallel.\nfind the measure of $\\angle a$.\n$m\\angle a = ? ^{\\circ}$

lines m and n are parallel.\nfind the measure of $\\angle a$.\n$m\\angle a = ? ^{\\circ}$

Answer

Explanation:

Step1: Identify the geometric relationship

Since lines $M$ and $N$ are parallel, the angle $a$ and the $55^{\circ}$ angle are consecutive interior angles.

Step2: Apply the consecutive interior angles theorem

Consecutive interior angles formed by parallel lines are supplementary, meaning their sum is $180^{\circ}$. $$m\angle a + 55^{\circ} = 180^{\circ}$$

Step3: Solve for the unknown angle

Subtract $55^{\circ}$ from both sides of the equation to find the measure of angle $a$. $$m\angle a = 180^{\circ} - 55^{\circ}$$ $$m\angle a = 125^{\circ}$$

Answer:

$m\angle a = 125^{\circ}$