Question

I need help finding the measures of angles 1, 2,3,4 and 5

Answer 1

First, let's start from the left with the angle that measures 88º and ∠1 (green line)

These two angles are a linear pair, which means that they add up to 180º, you can express it as:

`88º+\angle1=180º`

From this expression, you can calculate the measure of ∠1, just subtract 88º from 180º

`\begin{gathered} \angle1=180º-88º \\ \angle1=92º \end{gathered}`

∠1=92º

Second, the ∠5 and the angle that measures 81º. These angles are between two parallel lines crossed by a transversal line. The lines that link them make a Z shape (purple line).

These angles are alternate interior angles which makes them congruent, we can conclude that

∠5=81º

Third, from the triangle on the right we know 2 of its three angles and we know that the sum of the inner angles equals 180º, so we can calculate the missing angle as follows:

`\begin{gathered} \angle4+\angle5+64º=180º \\ \angle4+81º+64º=180º \\ \angle4+145º=180º \\ \angle4=180º-145º \\ \angle4=35º \end{gathered}`

∠4=35º

Fourth, ∠3, ∠4 and, the angle that measures 81º are supplementary angles (red line), which means that they add up to 180º, therefore you can calculate ∠3 as follows:

`\begin{gathered} \angle3+\angle4+81º=180º \\ \angle3+35º+81º=180º \\ \angle3+116º=180º \\ \angle3=180º-116º \\ \angle3=64º \end{gathered}`

∠3=64º

Fifth, ∠1, ∠2 and, ∠3 are the inner angles of the triangle on the left so they add up to 180º.

You can calculate ∠2 as follows:

`\begin{gathered} \angle1+\angle2+\angle3=180º \\ \angle2+64º+92º=180º \\ \angle2+156º=180º \\ \angle2=24º \end{gathered}`

∠2=24º

So

∠1=92º

∠2=24º

∠3=64º

∠4=35º

∠5=81º