Question

OFind the missingangle measures.Bm 41 =90°58°Аm 42 =23108°m 3 =Eoo

Answer 1

First you can calculate the measure of ∠1.

From triangle ABC, only one angle measurement is unknown, but we know that the sum of these three angles is equal to 180º, from this we can determine the measure of the missing angle as:

`\begin{gathered} 90+58+\angle1=180 \\ 148+\angle1=180 \\ \angle1=180-148 \\ \angle1=32º \end{gathered}`

So the measure from ∠1 is 32º

Next is to calculate ∠2.

As you can see in the image, angles ∠1 and ∠2 are in opposite sides of the same vertex, where both lines cross, they are vertical opposite angles. These type of angles are congruent, which means that they have the same measure so:

∠2=∠1=32º

Finally, from triangle CDE we know the measure of two out of three angles, using the same principle as for ∠1, we can calculate ∠3 as:

`\begin{gathered} 108+32+\angle3=180 \\ 140+\angle3=180 \\ \angle3=180-140 \\ \angle3=40 \end{gathered}`

So, ∠3=40º