Question

* Use the information given in the following figure to find :
x
angle B angle C

​

Answer 1

Step-by-step explanation:

$Value of x=22$

$\red {\angle B }\green {= 48\degree }∠B=48°$

$\red {\angle C }\green {= 83\degree }∠C=83°$

$</p><p>Given\: ABCD \: is \:a \: quadrilateral .GivenABCDisaquadrilateral.</p><p>$

$</p><p>\angle A = 90\degree∠A=90°</p><p></p><p>\angle B = (2x + 4)\degree∠B=(2x+4)°</p><p></p><p>\angle C = (3x - 5 )\degree∠C=(3x−5)°</p><p></p><p>\angle D = (8x - 15)\degree∠D=(8x−15)°$

$\boxed {\pink { sum \: of \: angles \: in \: quadrilateral = 360\degree }} </p><p>sumofanglesinquadrilateral=360°$

$\angle A + \angle B +\angle C + \angle D = 360\degree∠A+∠B+∠C+∠D=360°$

$\implies 90\degree + (2x+4)+(3x-5)+(8x-15)=360⟹90°+(2x+4)+(3x−5)+(8x−15)=360$

\implies 13x = 360 - 74⟹13x=360−74

\implies 13x = 286⟹13x=286

\implies x = \frac{286}{13}⟹x=

13

286

$</p><p>\implies 13x + 74 = 360⟹13x+74=360$

$\implies x = 22\: ---(1)⟹x=22−−−(1)$

$</p><p>\angle B = 2x + 4∠B=2x+4$

$angle B = 2\times 22 + 4 \: [ From \: (1) ]∠B=2×22+4[From(1)]$

$\angle B = 44 + 4 = 48\degree∠B=44+4=48°</p><p></p><p>\angle C = 3x -5∠C=3x−5</p><p>$

$</p><p>\angle C = 3\times 22 - 5 \: [ From \: (1) ]∠C=3×22−5[From(1)]$

$</p><p>\angle B = 88 - 5 = 83\degree∠B=88−5=83°$

$Therefore$

$\red {Value \: of \: x }\green { = 22 }Valueofx=22$

$\red {\angle B }\green {= 48\degree }∠B=48°$

$\red {\angle C }\green {= 83\degree }∠C=83°$

$</p><p>•••♪$