Question

Okay help me please

Answer 1

hope this helps

Explanation:

`m < ac = 80 \\ m < de = 24 \\ 80 - 24 = 76`

Answer 2

Therefore, the difference of arc measures
`\( m \overset{\frown}{AC} - m \overset{\frown}{DE} \)` is
`\( 80^\circ - 24^\circ = 56^\circ \).`

To solve this problem, we'll use the fact that the angle formed by two secants intersecting outside of a circle is equal to half the difference of the measures of the arcs that the secants intercept.

Given:

- The measure of angle
`\( ABC = 28^\circ \)`

- The measure of arc
`\( \overset{\frown}{AC} = 80^\circ \)`

- The measure of arc
`\( \overset{\frown}{DE} = 24^\circ \)`

The formula to find the angle formed by two intersecting secants is:

`\[ m \angle ABC = (1)/(2) (m \overset{\frown}{AC} - m \overset{\frown}{DE}) \]`

Now, we can calculate step by step:

1. Substitute the given values into the formula:

`\[ 28 = (1)/(2) (80 - m \overset{\frown}{DE}) \]`

2. Double both sides to eliminate the fraction:

`\[ 56 = 80 - m \overset{\frown}{DE} \]`

3. Solve for
`\( m \overset{\frown}{DE} \):`

`\[ m \overset{\frown}{DE} = 80 - 56 \]`

`\[ m \overset{\frown}{DE} = 24^\circ \]`

Since
`\( m \overset{\frown}{DE} \)` is already given as
`\( 24^\circ \),` the calculation confirms that the given values are consistent with the properties of intersecting secants.

Therefore, the difference of arc measures
`\( m \overset{\frown}{AC} - m \overset{\frown}{DE} \)` is
`\( 80^\circ - 24^\circ = 56^\circ \).`