Answer:
? = 45
Step-by-step explanation:
the inner and outer triangles are similar ( AA postulate )
Then the ratios of corresponding sides are in proportion, that is
[tex]\frac{56}{56+24}[/tex] = [tex]\frac{105}{105+?}[/tex] , that is
[tex]\frac{56}{80}[/tex] = [tex]\frac{105}{105+?}[/tex] ( divide numerator/denominator by 8 to simplify left side )
[tex]\frac{7}{10}[/tex] = [tex]\frac{105}{105+?}[/tex] ( cross- multiply )
7(105 + ? ) = 1050 ← distribute parenthesis on left side
735 + 7? = 1050 ( subtract 735 from both sides )
7? = 315 ( divide both sides by 7 )
? = 45
