Question

find the values of x and y. (the figure is not drawn to scale.) x = and y =

Explanation:

Step1: Use isosceles - triangle property

In the large isosceles triangle with the $70^{\circ}$ angle, the other two base - angles are equal. Let the base - angles be $a$. Using the angle - sum property of a triangle ($a + a+70^{\circ}=180^{\circ}$), we get $2a = 180^{\circ}-70^{\circ}=110^{\circ}$, so $a = 55^{\circ}$.

Step2: Find the value of $x$

In the right - angled sub - triangle, one of the non - right angles is part of the $55^{\circ}$ angle of the large isosceles triangle. Since the sum of angles in a right - angled triangle is $180^{\circ}$ and one angle is $90^{\circ}$, and another is $55^{\circ}$, then $x=55^{\circ}$.

Step3: Find the value of $y$

In the right - angled sub - triangle where $x$ is an angle, and the right angle is $90^{\circ}$, using the angle - sum property of a triangle ($x + y+90^{\circ}=180^{\circ}$). Substituting $x = 55^{\circ}$, we get $y=180^{\circ}-90^{\circ}-55^{\circ}=35^{\circ}$.

Answer:

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