Answer:
Part 1) [tex]x=71\°[/tex]
Part 2) [tex]x=90\°[/tex] and [tex]y=43\°[/tex]
Step-by-step 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
[tex]38\°+x\°+x\°=180\°[/tex]
solve for x
[tex]2x=180-38\\2x=142\\x=71\°[/tex]
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
[tex]x=90\°[/tex]
In the right triangle ABD
m∠ABD+y=90° -----> by complementary angles
substitute values
[tex]47\°+y=90\°\\y=90\°-47\°=43\°[/tex]
