Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Find the values of x and y.

Answer 1

x = 90 degrees, y = 43 degrees

Explanation:

Given: <C = 47 degrees

AB = AC

To find: x and y

proof:

in triangle ABC,

AC=AB

So, <B=<C=47 (angles opposite to equal sides of a triangle are equal)

<B=47 degrees

In triangle ABC,

<B + <C + 2y = 180 (angle sum property)

47 + 47 + 2y = 180

94 + 2y = 180

2y = 180-94

2y = 86

y = 86/2

y = 43

In triangle ABD,

<B + y + x = 180 (angle sum property)

47 + 43 +x = 180

90 +x = 180

x = 180-90

x = 90

Answer 2

`x=90^0\:,y=43^0`

Explanation:

1) This an Isosceles triangle then there are two congruent sides and two congruent angles:

`\angle B\cong \angle C= 47^(0)`

2) The Sum of Internal Angles are equal to 180º then:

`2y+47^0+47^0=180^0\Rightarrow 2y=180^0-94^0\Rightarrow 2y=86^0\Rightarrow y=43^0`

3) According to the figure
`\overline{AD}` bisects the ∠A then, by definition it is a perpendicular line, so x=90º and ∠D = 90º since it is its supplementary angle.

4) Proof

`\bigtriangleup ABD\Rightarrow \angle A+\angle B+\angle C=180\Rightarrow 43+47+90=180\Rightarrow 180=180 \: True`

`\bigtriangleup ADC\Rightarrow \angle A+\angle D+\angle C=180\Rightarrow 43+90+47=180\Rightarrow 180=180 \: True`