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11Alexandr11 [23.1K]
3 years ago
14

Use Vocabulary in Writing

Mathematics
1 answer:
NARA [144]3 years ago
8 0

x° = 43°

Solution:

The lines AD, BE and CF are intersecting lines.

Given m∠AGF = 47°, m∠BGC = 90°, m∠DGE = x°.

To find the value of x°:

Line BE and line CF intersect at the vertex G.

∠BGC and ∠FGE are vertical angles.

<u>Vertical angle theorem:</u>

If two angles are vertically opposite then they are congruent.

By vertical angle theorem, ∠BGC ≅ ∠FGE

⇒ m∠FGE = 90°

Sum of the angles in a straight line = 180°

In line AD,

m∠AGF + m∠FGE + m∠DGE = 180°

⇒ 47° + 90° + m∠DGE = 180°

⇒ 137° + m∠DGE = 180°

⇒ m∠DGE = 180° – 137°

⇒ m∠DGE = 43°

⇒ x° = 43°

Hence the value of x° is 43°.

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\bf ~~~~~~ \textit{Simple Interest Earned on 9 months}\\\\&#10;I = Prt\qquad &#10;\begin{cases}&#10;I=\textit{interest earned}\\&#10;P=\textit{original amount deposited}\to& \$900\\&#10;r=rate\to 2.9\%\to \frac{2.9}{100}\to &0.029\\&#10;t=years\to \frac{9}{12}\to &\frac{3}{4}&#10;\end{cases}&#10;\\\\\\&#10;I=900(0.029)\left( \frac{3}{4} \right)\\\\&#10;-------------------------------

\bf ~~~~~~ \textit{Simple Interest Earned on 6 months}\\\\&#10;I = Prt\qquad &#10;\begin{cases}&#10;I=\textit{interest earned}\\&#10;P=\textit{original amount deposited}\to& \$900\\&#10;r=rate\to 2.4\%\to \frac{2.4}{100}\to &0.024\\&#10;t=years\to \frac{6}{12}\to &\frac{1}{2}&#10;\end{cases}&#10;\\\\\\&#10;I=900(0.024)\left( \frac{1}{2}\right)

check their difference, that much.
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3 years ago
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