Question

Find the values of x and y.

Answer 1

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°.