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!
+1252 #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
+129852 (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°
