given only a compass and straightedge, Greeks were able to construct any geometric object they wished true or flase

The given statement is a FALSE statement.

Step-by-step explanation:

The ancient Greek mathematicians believed that any construction could be done by straightedge and a compass but when they actually tried to construct they observed that some polygons were constructed but most of them were not.

Later on, In algebra it was observed that:

A length is constructible if and only if it is a constructible number. An angle could be constructible if it's cosine is a constructible number. A number is constructible if it contain four basic arithmetic operation.

FALSE

Step-by-step explanation:

Examples:

regular heptagon

regular nexus

angle of measure 1°

Having only a compass and straightforwardness can not be constructed.