Question

1. if ( mangle c = 47 ), find the values of ( x ) and ( y ). ( x = 43, y = 47 ) ( x = 90, y = 47 ) ( x = 90, y = 43 ) ( x = 47, y = 43 )

Explanation:

Step1: Determine the value of \(x\)

In an isosceles triangle \(ABC\) (since \(AB = AC\)), \(AD\) is the median (because \(AB = AC\) and \(AD\) divides \(BC\) into two equal parts). In a triangle, the median from the vertex to the base of an isosceles triangle is also the altitude. So, \(\angle ADC=90^{\circ}\), thus \(x = 90\).

Step2: Calculate the value of \(y\)

In right - triangle \(ADC\), we know that \(\angle C = 47^{\circ}\) and \(\angle ADC=90^{\circ}\). Using the angle - sum property of a triangle (\(\angle A+\angle C+\angle ADC = 180^{\circ}\)), for \(\triangle ADC\), we want to find \(y\) (\(\angle CAD\)).

$$y+47 + 90=180$$

$$y=180-(90 + 47)$$

$$y = 43$$

Answer:

\(x = 90,y = 43\) (corresponds to the third option)