Questions: For the figure shown, find m∠1 and m∠2.

Transcript text: For the figure shown, find $\mathrm{m} \angle 1$ and $\mathrm{m} \angle 2$.

Solution

Solution Steps

Step 1: Find the supplementary angle to the 127° angle.

The line segment forming the 127° angle also forms another angle adjacent to it. These two angles are supplementary, meaning they add up to 180°. Let's call the unknown angle 'x'. Then:

x + 127° = 180° x = 180° - 127° x = 53°

Step 2: Find m∠1.

The sum of the angles in a triangle is 180°. In the top triangle, we have angles of 84°, ∠1, and 'x' which we found to be 53°. Therefore:

m∠1 + 84° + 53° = 180° m∠1 + 137° = 180° m∠1 = 180° - 137° m∠1 = 43°

Step 3: Find m∠2.

The line segment forming the 16° angle also forms another angle adjacent to it. These two angles are supplementary. This adjacent angle is part of the top triangle, and is formed by angles ∠1 and ∠2. So, this adjacent angle is equal to m∠1 + m∠2. Let's call the supplementary angle to 16° as 'y'. Then:

y + 16° = 180° y = 180° - 16° y = 164°

Since y = m∠1 + m∠2, and we already know m∠1 = 43°, we can write:

164° = 43° + m∠2 m∠2 = 164° - 43° m∠2 = 121°