Question

1. if m∠c = 47, find the values of x and y.

x = 90, y = 47
x = 47, y = 43
x = 90, y = 43
x = 43, y = 47

Explanation:

Step1: Identify the type of triangle and right - angle

Since $AD$ is the perpendicular bisector of $BC$ (implied by the equal - side markings), $\angle ADB=\angle ADC = 90^{\circ}$, so $x = 90$.

Step2: Use angle - sum property in right - triangle

In right - triangle $ADC$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Given $\angle C=47^{\circ}$ and $\angle ADC = 90^{\circ}$, we use the formula $\angle DAC+y=180^{\circ}-\angle ADC-\angle C$. So $y=180 - 90-47=43^{\circ}$.

Answer:

$x = 90,y = 43$