Question

Quiero saber como se hace la numero 4 por favor

Answer 1

For two triangles, m
`\angle 1`=
`30\textdegree`, m
`\angle2`=
`41\textdegree`, and m
`\angle 3`=
`96\textdegree`.

For m
`\angle 1` the two other angles are given (
`66\textdegree` and
`84\textdegree`). We know that the sum of the angles in a triangle is
`180\textdegree`. By solving this we get:

66+84+
`\angle 1`=180

150+
`\angle 1`=180

`\angle 1`=180-150

`\angle 1`=
`30\textdegree`

Therefore, m
`\angle 1` is
`30\textdegree`.

Now, for
`\angle2`, we can use the exterior angle theorem. The exterior angle theorem states that the measure of the exterior angle of a triangle is equal to the sum of two remote interior angles.

So, 43 +
`\angle2` = 84

`\angle2`=84-43

`\angle2` =41

Therefore, m
`\angle2` is
`41\textdegree`

Now, for
`\angle 3`, we can again use the fact that the sum of the angles in a triangle is
`180\textdegree`.

41+43+
`\angle 3` =180

84+
`\angle 3` =180

`\angle 3`=180-84

`\angle 3`= 96

Therefore, m
`\angle 3` is
`96\textdegree`