Mathematics: Convert 0.31 to binary then back to base 10 and work out the error

Convert 0.31 to binary then back to base 10 and - id031101028423, genyjoannerubiera

kristygodwin

29.09.2021

$m\angle a=35^{\circ}$

$m\angle b=55^{\circ}$

$m\angle c=110^{\circ}$

Step-by-step explanation:

We have been given a diagram. We are asked to find the measures of angles a, b and c.

Upon looking at our given diagram, we can see that angle a and 35 degrees angles are vertical angles.

Since measures of vertical angles are always equal, therefore, measure of angle of a is 35 degree.

To solve for angle b, we will use angle sum property.

$m\angle a+m\angle b+90^{\circ}=180^{\circ}$

$35^{\circ}+m\angle b+90^{\circ}=180^{\circ}$

$m\angle b+125^{\circ}=180^{\circ}$

$m\angle b+125^{\circ}-125^{\circ}=180^{\circ}-125^{\circ}$

$m\angle b=55^{\circ}$

Therefore, measure of angle b is 55 degrees.

To find measure of angle c, we will use exterior angle theorem. We know that measure of an exterior angle is equal to two non adjacent angles.

To find measure of c, we will subtract 70 degrees from 180 degrees as:

$m\angle c=180^{\circ}-70^{\circ}$

$m\angle c=110^{\circ}$

Therefore, measure of angle c is 110 degrees.

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