Question

Example 21: Find angle w, x, y and z? 519​

Answer 1

Explanation:

Answer:

given that BC=BD

so LCDB =LCBD=62°=w

now, LCDA=90° because angles made on the circumference of a circle from the end points of the diameter are all 90°

therefore,

x+w=90°

x=90°-w

=90°-62°

=28°

therefore, x=28°

again, we know that the median of a isosceles triangle bisect the angle equally.

therefore, LDCB=2z

now, LDCB =180°-(w+62°)=180°-124°=56°

therefore, LDCB=56°

therefore, 2z=56°

z=28°

now in triangle ADC,

y+(x+w)+z=180°

=>y+90°+28°=180°

=>y=180°-118°

therefore, y=62°

therefore, w=62°,x=28°, y=62° and z=28°