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3 years ago

What is the length of segment SR?

Mathematics

1 answer:

stiks02 [169]3 years ago

6 0

ST = ST (Common)

RT = TQ (Given)

∠ RTS = ∠ SQT (Both 90°)

So, ∆ RTS ≅ ∆ QTS (By SAS congruency rule)

So, RS = QS (By C.P.C.T.)

=> 2x + 8 = 8x - 4

=> 8 + 4 = 8x - 2x

=> 12 = 6x

=> 12/6 = x

=> 2 = x

SR = 2x + 8 (Given)

=> SR = 2(2) + 8 (Putting the value of x)

=> SR = 4 + 8

=> SR = 12

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This Question: 1 pt

zhenek [66]

$\huge{ \mathfrak{ \underline{ Answer }\: \: ✓ }}$

Angles forming linear pair are :

$\mathrm{\angle EFG \: \: and \: \: \angle GFH}$

And we know, they are supplymentary

$\mathrm{\angle EFG \: + \: \angle GFH} = 180 \degree$
$3n +1 9 \degree+ 2n + 36\degree = 180 \degree$
$5n + 55\degree = 180\degree$
$5n = 125\degree$
$n = 25\degree$

So, the measures of the given angles are :

$\mathrm{\angle EFG } = 3n + 19$
$\mathrm{ \angle EFG = (3 \times 25\degree) + 19}$
$\mathrm{ \angle EFG = 75 \degree+ 19\degree}$
$\mathrm{ \angle EFG = 94\degree}$

And

$\mathrm{ \angle GFH = 2n + 36}$
$\mathrm{ \angle GFH = (2 \times 25\degree) + 36\degree}$
$\mathrm{ \angle GFH = 50\degree + 36\degree}$
$\mathrm{ \angle GFH = 86\degree }$

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