a) The measure of the angle of turn symmetry is 180⁰
b) The measures of the angles of turn symmetry are 90⁰, 180⁰ and 270⁰.
What is turn of angle of symmetry?
Angles of turn symmetry refer to the angles by which a geometric figure can be rotated to coincide with its original shape.
For the first figure
a) The parallelogram can be rotated 90⁰ twice to coincide with the original figure
The angles of turn of symmetry is
90⁰ + 90⁰ = 180⁰
b) For the figure 2
The semi-circle is rotated 4 times to coincide with the original shape.
Each rotation = 360/4
= 90⁰
The vertical semicircle turned 90⁰ to give horizontal one.
The vertical semicircle turned 180⁰ to give another vertical in opposite orientation.
And turned 270⁰ to produce horizontal in opposite orientation.
Therefore, the angles of turns are 90⁰, 180⁰ and 270⁰.