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1 year ago

In the following diagram HI || JK.What is the measure of Angles are not necessarily drawn to scale.

Mathematics

1 answer:

Nadya [2.5K]1 year ago

4 0

ANSWER

xº = 52º

EXPLANATION

Since segments HI and JK are parallel, we can see segment AK as a transversal:

So angle JKA and angle HIA are <em>corresponding angles</em> and they are congruent.

Then we have triangle HAI, and we have two of the angle's measures. The sum of the measures of the interior angles of a triangle is 180º:

$xº+66º+62º=180º$

Solving for x:

$\begin{gathered} xº+128º=180º \\ xº=180º-128º \\ xº=52º \end{gathered}$

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2 years ago

ABCD is a rectangle. The measure of angle BCE is 4x-23 and the angle measure of angle DCE is 5+5x. Find the measure of angle BEC

Temka [501]

<h2>Explanation:</h2><h2></h2>

The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:

$\angle BCE=\beta \\ \\ \angle DCE=\theta$

Every internal angle of any rectangle measures 90 degrees, so:

$\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12$

So:

$\beta=4x-23=4(12)-23=25^{\circ}$

So the measure of angle BEC can be found as follows:

We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So

$\angle EBC=\beta$

The sum of internal angles of any triangle add up to 180 degrees, so:

$\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}$

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3 years ago

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3 years ago

Y= 3x+7<br> y = -2x - 3<br> Whats the x and y for the solution

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Answer:

x=-2, y=1

Step-by-step explanation:

y=3x+7

y=-2x+3

Set the two equations equal to each other:

3x+7=-2x-3

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5x+7=-3

Subtract 7 from both sides:

5x=-10

Divide both sides by 5:

x=-2

Plug back into one of the original equations to find y:

y=3(-2)+7=-15+7=1

Hope this helps!

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3 years ago