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

Answer:

$x^{\circ}=35^{\circ}\\ \\y^{\circ}=55^{\circ}$

Step-by-step 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

$x^{\circ}=\dfrac{1}{2}\cdot 70^{\circ}=35^{\circ}$

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

$y^{\circ}=90^{\circ}-35^{\circ}=55^{\circ}$