1) Five of the six interior angles of a hexagon have measures 111◦ , 122◦ , 133◦ , 144◦ , and 155◦ . What is the measure of the unknown interior angle?

2) The length of a diagonal of a square is 3 √ 2. What is the area of the square?

3) Quadrilateral ABCD is inscribed in a circle. We know ∠BAD = 51◦ and ∠ABC = 66◦ . Find ∠ADC.

4) DC is tangent to circle O at C. If ∠ABC = 57◦ , ∠BAC = 60◦ , and ∠BCA = 63◦ , then what is the measure of ∠ACD?

5) Triange ABC is inscribed in circle O. We know ∠AOB = 106◦ , ∠AOC = 124◦ . Find the measure of ∠BAC.

Thanks!

Guest Mar 22, 2020

#1**+2 **

**#1 Answer: 55 degrees**

**#1 Explanation:**

The angles added up are 665 degrees.

The angles of a hexagon add to 720 degrees.

The missing angle is therefore 55 degrees.

**#2 Answer: 9 (square units)**

**#2 Explanation:**

The diagonal of a square forms a right triangle, with the diagonal as hypotenuse and two sides as legs.

The two sides are equal.

If we let one side have length x, then

x^2+x^2=(3sqrt2)^2

by Pythagorean Theorem.

2x^2=18

x^2=9

The area of the square is x^2, and we found it to be 9.

A useful formula is that the area of the square when you have the diagonal is (diagonal^2)/2

You are very welcome!

:P

CoolStuffYT Mar 22, 2020

#2**+1 **

(3)

Opposite angles in a cyclic quadrilateral are supplementary

Therefore......

angle ABC + angle ADC = 180

66 + angle ADC = 180 subtract 66 from both sides

angle ADC = 114°

CPhill Mar 22, 2020