When two angles have the same number of markers, this indicates that the angles are congruent.
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Practice makes perfect
Let's take a look at the given diagram presenting two triangles. On the diagram, the angle markers indicate congruent angle pairs.
We can see that two angles of â–³ ABC are congruent to two angles of â–³ FHG.
∠B&≅ ∠H
∠A&≅ ∠F
Now let's recall the Third Angle Theorem.
Third Angle Theorem
If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
According to the theorem, since our triangles share two angles, the third angles of these two triangles are also congruent.
∠G≅∠C
This means that these angles have the same measures so m∠G is equal to m∠C. Notice that the measure of ∠C and an expression for the measure of ∠G are given. Therefore, by using the congruence, we can set up an equation for x.
