Answer:
x = 16
y = 105°
Step-by-step explanation:
Given:
∆ABC ~ ∆XYZ
a = 24
Required:
Value of x and y
Solution:
Since ∆ABC ~ ∆XYZ, therefore:
<A ≅ <X
<B ≅ <Y
<C ≅ <Z
Also, the ratio of their Corresponding sides will be the same. That is,
[tex] \frac{21}{14} = \frac{15}{10} = \frac{24}{x} [/tex]
Find the value of x using,
[tex] \frac{15}{10} = \frac{24}{x} [/tex]
Cross multiply
[tex] 15*x = 24*10 [/tex]
[tex] 15x = 240 [/tex]
Divide both sides by 15
[tex] x = \frac{240}{15} [/tex]
[tex] x = 16 [/tex]
y = 180° - 75°(linear pair/angles on a straight line theorem)
y = 105°
