If two adjacent sides of parallelogram are 20 cm and 27 cm and the shorter diagonal is 23 cm then the measure of larger angles in the parallelogram is 123.75°.
Given Two adjacent sides are 20 cm and 27 cm. The shorter diagonal is 23 cm. and we need to find the measure of larger angle.
From law of cosines
[tex]c^{2} =a^{2} +b^{2} -2abcos d[/tex]
where c is the opposite side of angle, a and b are other sides and d is the angle.
[tex]23^{2} =20^{2} +27^{2} -2*20*27cos d[/tex]
where 23 is the length of shorter diagonal
529=400+729 - 1080 cos d
1080 cos d=600
cos d=600/1080
cos d=0.55
d=[tex]cos^{-}[/tex]0.55
d=56.25°
Adjacent angle=180-56.25
=123.75°
Largest angle=123.75°.
Hence the larger angle of parallelogram having sides 20 and 27cm is 123.75°.
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