Question

use the information information given in the following figure to find:

- x
- angle B and C

this is my question

Answer 1

Answer:

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

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

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

Step-by-step explanation:

$Given\: ABCD \: is \:a \: quadrilateral .$

$\angle A = 90\degree$

$\angle B = (2x + 4)\degree$

$\angle C = (3x - 5 )\degree$

$\angle D = (8x - 15)\degree$

$\boxed {\pink { sum \: of \: angles \: in \: quadrilateral = 360\degree }}$

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

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

$\implies 13x + 74 = 360$

$\implies 13x = 360 - 74$

$\implies 13x = 286$

$\implies x = \frac{286}{13}$

$\implies x = 22\: ---(1)$

$\angle B = 2x + 4$

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

$\angle B = 44 + 4 = 48\degree$

$\angle C = 3x -5$

$\angle C = 3\times 22 - 5 \: [ From \: (1) ]$

$\angle B = 88 - 5 = 83\degree$

Therefore.,

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

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

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

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Answer 2

Step-by-step explanation:

Valueofx=22

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

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

Step-by-step explanation:

Given\: ABCD \: is \:a \: quadrilateral .GivenABCDisaquadrilateral.

\angle A = 90\degree∠A=90°

\angle B = (2x + 4)\degree∠B=(2x+4)°

\angle C = (3x - 5 )\degree∠C=(3x−5)°

\angle D = (8x - 15)\degree∠D=(8x−15)°

\boxed {\pink { sum \: of \: angles \: in \: quadrilateral = 360\degree }}

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 + 74 = 360⟹13x+74=360

\implies 13x = 360 - 74⟹13x=360−74

\implies 13x = 286⟹13x=286

\implies x = \frac{286}{13}⟹x=

13

286

\implies x = 22\: ---(1)⟹x=22−−−(1)

\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°

\angle C = 3x -5∠C=3x−5

\angle C = 3\times 22 - 5 \: [ From \: (1) ]∠C=3×22−5[From(1)]

\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°

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