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3 years ago

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What is m∠A ? Enter your answer in the box. ° Triangles A B E and D C E share vertex E. Angle B is 18 degrees. Angle C is 43 deg

rees. Angle D is 35 degrees.

2 answers:

Allisa [31]3 years ago

5 0

Answer: The measure of angle A is 60 degree.

Explanation:

It is given that the Triangles A B E and D C E share vertex E. Angle B is 18 degrees. Angle C is 43 degrees. Angle D is 35 degrees.

According to angle sum property, the sum of angles of a triangle is always 180 degree.

In triangle CDE,

$\angle ECD+\angle CDE+\angle DEC=180^{\circ}$

$43^{\circ}+35^{\circ}+\angle DEC=180^{\circ}$

$78^{\circ}+\angle DEC=180^{\circ}$

$\angle DEC=180^{\circ}-78^{\circ}$

$\angle DEC=102^{\circ}$

According to opposite vertical angle property.

$\angle AEB=\angle DEC$

$\angle AEB=102^{\circ}$

Use angle sum property is triangle ABE.

$\angle ABE+\angle BEA+\angle EAB=180^{\circ}$

$\angle ABE+102^{\circ}+18^{\circ}=180^{\circ}$

$\angle ABE+120^{\circ}=180^{\circ}$

$\angle ABE=60^{\circ}$

Therefore, the measure of angle A is 60 degree.

borishaifa [10]3 years ago

5 0

Answer:

60 degrees

Step-by-step explanation:

It is given that the Triangles A B E and D C E share vertex E. Angle B is 18 degrees. Angle C is 43 degrees. Angle D is 35 degrees.

According to angle sum property, the sum of angles of a triangle is always 180 degree.

In triangle CDE,

According to opposite vertical angle property.

Use angle sum property is triangle ABE.

Therefore, the measure of angle A is 60 degrees

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3 years ago

Find the domain of the function y = 3 tan(23x)

solmaris [256]

Answer:

$\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

In other words, the $x$ in $f(x) = 3\, \tan(23\, x)$ could be any real number as long as $x \ne \displaystyle \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right)$ for all integer $k$ (including negative integers.)

Step-by-step explanation:

The tangent function $y = \tan(x)$ has a real value for real inputs $x$ as long as the input $x \ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

Hence, the domain of the original tangent function is $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

On the other hand, in the function $f(x) = 3\, \tan(23\, x)$ , the input to the tangent function is replaced with $(23\, x)$ .

The transformed tangent function $\tan(23\, x)$ would have a real value as long as its input $(23\, x)$ ensures that $23\, x\ne \displaystyle k\, \pi + \frac{\pi}{2}$ for all integer $k$ .

In other words, $\tan(23\, x)$ would have a real value as long as $x\ne \displaystyle \frac{1}{23} \, \left(k\, \pi + \frac{\pi}{2}\right)$ .

Accordingly, the domain of $f(x) = 3\, \tan(23\, x)$ would be $\mathbb{R} \backslash \displaystyle \left\lbrace \left. \frac{1}{23}\, \left(k\, \pi + \frac{\pi}{2}\right) \; \right| k \in \mathbb{Z} \right\rbrace$ .

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Answer:

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Step-by-step explanation:

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