11. m ∠ BCE = 25 °
m ∠BAD = 39°
12. n = 11. 5°
13. The quadrilaterals are rectangle and parallelogram. Option A and C
14. HK = 8cm
<h3>How to determine the angles</h3>
11. From the figure shown, we have that;
m ∠ EBC = 27°
m ∠ ADE = 52°
To find
m ∠ BCE
Note that m ∠ ADE is alternate and equal to m∠ DEC = 52 and is also on a straight line with ∠BEC
52 + ∠BEC = 180°
∠BEC = 180 - 52° = 128°
Remember that ∠BEC, ∠ BCE and ∠ EBC are angles in a triangle which sum up to 180°
128° + ∠ BCE + 27° = 180°
∠ BCE = 180 ° - 155°
∠ BCE = 25 °
To determine m ∠BAD
65° + 76 + m ∠BAD = 180° , sum of angles in a a triangle
m ∠BAD = 180 - 141
m ∠BAD = 39°
12. Value of n is gotten by equating the two lengths
( 10n + 19) = (12n - 4)
collect like terms
10n - 12n = -4 - 19
- 2n = -23
n = -23/-2
n = 11. 5°
13. The only quadrilaterals with congruent diagonals are;
14. To find line HK
Substract the shortest line, IJ from the longest line GL
HK = GL - IJ
HK = 15 - 7
HK = 8cm
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