Answer:
See below ~
Step-by-step explanation:
Let's get started!
Part (a) :
Statement 1 : ∠A = ∠E = 90° (indicated in diagram)
Statement 2 : ∠C = ∠C (common angle)
⇒ ΔABC ~ ΔBDC (AA similarity)
Part (b) :
Now that we have proved the triangles to be similar, we can take their corresponding sides in proportion.
⇒ [tex]\frac{EC}{AC} = \frac{ED}{AB}[/tex]
⇒ [tex]\frac{160}{160+50} = \frac{120}{AB}[/tex]
⇒ [tex]\frac{16}{21} = \frac{120}{AB}[/tex]
⇒ [tex]AB = \frac{120\times21}{16}[/tex]
⇒ [tex]AB = \frac{2520}{16}[/tex]
⇒ AB = 157.5
