Question

Find the value of the missing variables.

(Angles of Chords Secants and Tangents)

Look in the attached file to see the problem

Answer 1

`x^(\circ)=35^(\circ)\\ \\y^(\circ)=55^(\circ)`

Explanation:

The measure of arc which the right triange cuts from the circle is
`70^(\circ),` this means the central angle has the same measure.

Angle with measure
`x^(\circ)` is inscribed angle subtended on the given arc. Its measure is half the measure of the central angle, hence

`x^(\circ)=(1)/(2)\cdot 70^(\circ)=35^(\circ)`

Angles with measures
`x^(\circ)` and
`y^(\circ)` are complementary angles (add up to 90°), so

`y^(\circ)=90^(\circ)-35^(\circ)=55^(\circ)`