ACT Math 5.3 Plane Geometry
ACT Math: Plane Geometry Drill 5, Problem 3. What is the measure of Angle GHJ?
|ACT Math||Plane Geometry|
|ACT Mathematics||Plane Geometry|
|Congruence||Make geometric constructions|
|Foreign Language||Arabic Subtitled|
|Geometry||Congruence and constructions|
Make geometric constructions
Properties of plane figures
The concept of proof and proof techniques
|Product Type||ACT Math|
and angle I = 85°, and they want us to use that information to find the measure of GHJ.
First we should try to find GHJ's supplementary
angle, the one that'll form a straight angle and help it add up to 180 degrees... either
angle IHJ or FHG will do. Let's find angle FHG, because... well, it's closer
Since FG and IJ are parallel, angles I and G are alternate interior angles.
In other words, they're on opposite-inside sides of the transversal, the line that cuts
across two parallel lines. That means that they are congruent, or the
same, and since I measures 85 degrees, that means G does too.
We already know angle F, so now we just have to solve for the final angle in the triangle,
which is angle FHG. To do that, we add angles F and G, and subtract that from 180 degrees.
We get 55 degrees as our answer.
That's only the supplementary angle, remember... our last step is to subtract 55 from 180.
We get 125 degrees, which means that our answer is C.