In ∆DEF, DE = EF. One of the equal angles is 50°.Find angles x, y and z.
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In ∆DEF, DE = EF. One of the equal angles is 50°.Find angles x, y and z.
In ∆DEF, DE = EF. One of the equal angles is 50°.Find angles x, y and z.
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Answer:
z=50°, x=100°, y=130°
Step-by-step explanation:
Since, one of the equal angles of the given isosceles triangle is 50°
Then,
angle EDF = angle DFE = 50°
angle z = angle DFE = 50°
z = 50°
Now, angle FDE + angle DEF + angle DFE = 180 (angle sum property)
50 + angle DEF + 50 = 180
100 + angle DEF = 180
angle DEF = 180 - 100
angle DEF = 80°
angle DEF + angle x = 180 (linear pair)
80 + x = 180
x = 180 - 80
x = 100
angle DEF + z = y (exterior angle property)
80 + 50 = y
y = 130°