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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.

 Mar 6, 2021
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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

 Mar 6, 2021

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