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(5)
Let the other acute angle = x.
One angle = 60 and other = 90.
Sum of angles of triangle = 180.
=> x + 60 + 90 = 180
=> x + 150 = 180
=> x = 30
Hence, other angle is 30°.
(6)
Let the angles be a,b,c.
Sum of angles in a triangle = 180
a + b + c = 180---- (i)
One angle is equal to sum of other two sides.
a + b = c ---- (2)
Solve (1) and (2),
=> 2(a + b) + c = 180 + c
=> a + b = 90
Hence, it is right angled triangle.
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Answer:
5) another acute angle = 30°
6) proof in the attachment
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