1.

A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.

Answer»

Three angles are acute angle and each measuring is 75° means

\(\angle\)A = \(\angle\)B = \(\angle\)C = 75°

(Acute angle is angle whose measuring is greater than 0 and less than 90.)

As we know that, Sum of all four angles of quadrilateral is 360o

\(\angle\)A  + \(\angle\)B + \(\angle\)C + \(\angle\)D = 360°

75° + 75° + 75° + D = 360°

\(\angle\)D = 360° - (75° + 75° + 75°)

= 360° - 225°

= 135° 

So, fourth angle of quadrilateral is 135°.



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