Question

Calculate the fourth angle of the quadrilateral whose other three angles are in the order 97 degrees, 82degrees,102degrees

Answer 1

Answer:

79

Step-by-step explanation:

sum of all angles in quadrilateral= 360

so 97+82+102+x=360

281+x=360

x=360-281

x=79

Answer 2

Question:

Calculate the fourth angle of the quadrilateral whose other three angles are in the order 97 °, 82°,102°

To Find:

Angle D

Solution:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

$\textsf{In the given figure }\angle A = 97^{\circ} , \angle B = 82^{\circ},\angle C= 102^{\circ},$

$x+97+82+102=360\textsf{(since\:sum\:of\:angles\:of\:a\:quadrilateral\:is\:360)}\\\\\\x+281=360\\\\\\x=360-281\\\\\\x=79^{\circ}\\\\\\\boxed{x=79^{\circ}}$

Answer:

The fourth angle = 79°