# Math Help - Angles from Tangents

1. ## Angles from Tangents

Hey guys!

I'm in need of some help again! :/ We're learning about tangents right now, I've got a test tomorrow morning. I've spent at least 5 hours in these 4 problems these past two days, and all I could figure out was 14 (55º).

2. Hi Gui, can you explain, the angles 20,35, 70 and 120 degrees.
Between AG and AF, I can see 20 and 70 degrees. That is not clear to me.

3. Originally Posted by Gui
Hey guys!

I'm in need of some help again! :/ We're learning about tangents right now, I've got a test tomorrow morning. I've spent at least 5 hours in these 4 problems these past two days, and all I could figure out was 14 (55º).

Hi Gui,

[12] Find m $\angle GAF$

This angle is formed by the intersection of secants AF and AG.

The measure of the angle is equal to the difference of the measures of the intercepted arcs.

[13] Find $\angle GMH$

This angle is formed by the tangent MH and chord MG.

The measure of the angle is equal to one-half the measure of its intercepted arc.

The intercepted arc here is $\widehat{MG}$.
You already know the measure of $\widehat{FG}=70$

You can find $\widehat{MF}$ easily by subtracting arcs BC, CM, and FG from 180 since BG is a diameter.

Then add arcs FG and MF to get the intercepted arc you need. Then take half of it for your answer.

[14] Find m $\angle AEM$

This angle is formed by the intersection of two chords.
The measure of the angle is equal to one-half the sum of the measures of the intercepted arcs.

The intercepted arcs are CM and FG.