Question

I need all steps to be shown and the values of x and y. I’m so confused, please help!

Answer 1

Part 1)
`x=71\°`

Part 2)
`x=90\°` and
`y=43\°`

Explanation:

Part 1) we know that

An isosceles triangle has two equal sides and two equal interior angles

The triangle of the figure is an isosceles triangle

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

so

`38\°+x\°+x\°=180\°`

solve for x

`2x=180-38\\2x=142\\x=71\°`

Part 2) we know that

The triangle of the figure ABC is an isosceles triangle

because

AB=AC

so

m∠ABD=m∠ACD=47°

The segment AD is the height of the triangle

therefore

Angle x is a right angle

`x=90\°`

In the right triangle ABD

m∠ABD+y=90° -----> by complementary angles

substitute values

`47\°+y=90\°\\y=90\°-47\°=43\°`