Question

Please assist me with this question

Answer 1

? = 45

Explanation:

the inner and outer triangles are similar ( AA postulate )

Then the ratios of corresponding sides are in proportion, that is

`(56)/(56+24)` =
`(105)/(105+?)` , that is

`(56)/(80)` =
`(105)/(105+?)` ( divide numerator/denominator by 8 to simplify left side )

`(7)/(10)` =
`(105)/(105+?)` ( 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