Answer:
x= 38
y= 71
Step-by-step explanation:
The triangle shown in the figure is an isosceles triangle, a triangle having two sides equal.
The two sides marked with a "dash" are said to be equal.
STEP I:
If we label off the triangle as ABC with AD being the extended length (containing 108°).
We'll get,
AB = AC
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STEP II:
*Property*
"If two sides of a triangle are equal their corresponding base angles are equal too."
=> ∠BAC = ∠BCA . . . . (¡)
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STEP III:
From the figure, ∠BCA is equal to y.
*Property*
"Two angles on a straight line sum up to 180°"
∠BAC can be found out by subtracting 109° from the straight angle (180°).
=> ∠BAC = 180 - 109
=> ∠BAC = 71°
Substituting these values in eqn. (¡):
71 = y
Hence, the value of y is 71°
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STEP IV:
*Property*
"The exterior angle(angle on the extended side) of a triangle is equal to the sum of it's interior opposite angles."
Here,
- Interior angles = x and y (= 71)
- Exterior Angle = 109°
=> 109 = x + 71
=> 109 - 71 = x
=> x = 38°
Hence, the value of x is 38°.
