Answer: ∠E=55°
Step-by-step explanation:
Concept
- In all similar triangles, their corresponding angle will be the same value
- Triangle angle sum theorem: the three interior angles of a triangle add up to 180°
Given
- Two pairs of corresponding angles
- Two similar triangles
Solve
(6x-15)+4x=(5x-1)+4x ⇔ Add the angles up
6x-15=5x-1 ⇔ Subtract 4x on both sides
x-15=-1 ⇔ Substract 5x on both sides
x=14 ⇔ Add 15 on both sides
180-4x-(5x-1) ⇔ Find ∠E by subtracting the other two angles from 180
=180-4(14)-([5(14)-1]
=180-56-69
=55°
Hope this helps!! :)
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