1.Four of the five interior angles of a pentagon have measures 111◦ , 122◦ , 133◦ , and 144◦ . What is the measure of the unknown interior angle?
2. The area of a square is 18. What is the length of its diagonal?
3. Quadrilateral ABCD is inscribed in a circle. We know ∠BAD = 55◦ and ∠ABC = 56◦. Find ∠ADC.
1) Pentagon has interior angles that sum to (n-2)*180 = 540 take it from here
2) area of a square = l * w but l and w are equal
so area = l^2
18 = l^2 then you can find 'l'
diagonal is Pythag theorem diagonal = l^2 + l^2 Take it from here
3.) Opposite angles in an inscribed quad are supplementary (add to 180 ) Take it from here