Question

The fourth angle of the quadrilateral that has three acute angles isA)rightB)straightC)obtuseD)acutePlease answer

Answer 1

obtuse angle is the answer
let the 3 acute angles be 80, 85,60 and fourth angle be x
then, the sum of interior angles in a quadrilateral is 360
80+85+60+x= 360
225+x=360
x=360-225
x=135
135 is an obtuse angle
so the fourth angle will be obtuse angle
I think this answer is help full to you

Answer 2

The fourth angle of a quadrilateral have three acute angles will be an obtuse angle

Explanation:

1. let the quadrilateral be denoted by 'ABCD' with its four angles A, B, C and D respectively.
2. now given that three angles are acute (that is angle measures less than $90$° ) let the and A, B, and C be given by ,                                                          $A=90-x,\ \ \ \ B=90-y,\ \ \ \ C=90-z$                                                                   where x, y and z are positive.
3. then as we know that sum of all angles of a quadrilateral is $360$° we get,   $A+B+C+D=360$                                                                                                     $90-x+90-y+90-z+D=360\\D=360-270+(x+y+z)\\D=90+(x+y+z)$              
4. since x, y, and z are positive we get the value of fourth angle (D) to be more than $90$° for all such possible cases.
5. hence, the angle is obtuse and correct answer is option (c)