Max is correct when he says he saved 15% altogether
Let assume that each item costs $100
With a 10% discount, he would pay $90
With a 20% discount, he would pay $80
The total amount he bought the items with the discount = $90 + $80 = $170
Without the discount, he would have paid = $100 + $100 = $200
Amount saved = $200 - $170 = $30
Percentage savings = x 100 = 15%
Max saved 15% in total
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Part 1
Focus on triangle ABC.
Since AB is a diameter of the circle, this means angle ACB is 90 degrees. Refer to Thale's Theorem. Or you could use the inscribed angle theorem. Thale's theorem is a special case of the inscribed angle theorem.
Minor arc CB is 48 degrees. Use the inscribed angle theorem to see that angle CAB is 48/2 = 24 degrees.
Therefore, angle CBA = 90 - (angle CAB) = 90 - 24 = 66 degrees
<h3>Answer: 66</h3>========================================================
Part 2
Inscribed angle CBA was found to be 66 degrees back in part 1.
This doubles to 132 degrees to represent minor arc AC.
Or you could note that:
minor arc AC = 180 - (minor arc CB) = 180 - 48 = 132
Inscribed angle BCD is 48 degrees. This doubles to 96 degrees when using the inscribed angle theorem, and this is the measure of minor arc CBD.
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Here's what we know about the arc measures of the circle
These three arcs, along with minor arc AD, will add up to get a full 360 degree circle. Check out the diagram below.
Adding those 3 pieces gets us 132+48+96 = 276
This means minor arc AD has to be 360 - 276 = 84 degrees
Then use the inscribed angle theorem one more time to divide the minor arc AD in half to get the inscribed angle ACD
84/2 = 42
<h3>Answer: 42</h3>