Q (i) A quadrilateral has three acute angles each measuring 85 Find the measure of the fourth - Maths - Understanding Quadrilaterals

Question

Q (i) A quadrilateral has three acute angles each measuring 85
° Find the measure of the fourth angle
(ii) The four angles of quadrilateral are 2(x-10) ° , (x+30)
° , (x+50) ° and 2x ° Find all the four angles

Shruti Tyagi · Accepted Answer

Dear student,
i) Let the fourth angle be 'x'Now, 85°+85°+85°+x=360°     --[sum of angles of quad is 360°]⇒255°+x=360°⇒x=360°-255°⇒x=105°ii) Since sum of angles of quad is 360°2x-10+x+30+x+50+2x=360°⇒2x-20+x+30+x+50+2x=360°⇒6x+60°=360°⇒6x=300°⇒x=50°Thus the angles of quad
 are2x-10=250-10=2×40=80°x+30=50+30=80°x+50=50+50=100°2x=2×50=100°
Regards

Q. (i) A quadrilateral has three acute angles each measuring 85 ° . Find the measure of the fourth angle. (ii) The four angles of quadrilateral are 2(x-10) ° , (x+30) ° , (x+50) ° and 2x ° . Find all the four angles.

Q. (i) A quadrilateral has three acute angles each measuring 85 $°$ . Find the measure of the fourth angle.
(ii) The four angles of quadrilateral are 2(x-10) $°$ , (x+30) $°$ , (x+50) $°$ and 2x $°$ . Find all the four angles.