Answer:
<em>x = 9</em>
Step-by-step explanation:
Vertical angles are congruent, so their measures are equal.
4x + 6 = 7x - 21
Subtract 7x from both sides.
-3x + 6 = -21
Subtract 6 from both sides.
-3x = -27
Divide both sides by -3.
x = 9
(5, 3) (-6, 3)
The slope is 0 Slope = m = (Y2<span> -Y</span>1<span>) </span>÷<span> (X</span>2<span> -X</span>1<span>) (Y2 -Y1)=0
SO, the distance is just the difference in the x values.
distance = 5 --6 = 11
</span>
The answer is: he can eat 48 hotdogs in 12 minutes. How? Well, first, to find the amount of hotdogs he can eat in 1 min. you have to divide 32 by 8, and obviously you get 4. Now you multiply 4 by 12 and you get your answer, which is 48. Good luck with your homework!
a. The value of x is 7
b. The measure of ∠1 is 99°
<h3>Calculating angles </h3>
From the question, we are to solve for x
From the given diagram, we can write that
m∠NMQ + m∠MQN + m∠QNM = 180° (<em>Sum of angles in a triangle</em>)
From the given information,
m∠NMQ = 5x +19
m∠MQN = 8x -11
m∠QNM = 11x + 4
Then,
5x + 19 + 8x -11 + 11x + 4 = 180
Collect like terms
5x + 8x + 11x = 180 - 19 + 11 - 4
24x = 168
∴ x = 168/24
x = 7
Hence, the value of x is 7
b.
Measure of ∠1 + m∠QNM = 180° (<em>Sum of angles on a straight line</em>)
∴ Measure of ∠1 = 180° - m∠QNM
But m∠QNM = 11x + 4
∴ m∠QNM = 11(7) + 4
m∠QNM = 77 + 4
m∠QNM = 81°
Then,
Measure of ∠1 = 180° - 81°
Measure of ∠1 = 99°
Hence, the measure of ∠1 is 99°
Learn more on Calculating angles here: brainly.com/question/25716982
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Answer:
58 degrees
Step-by-step explanation:
In a rectangle, the two diagonals form four isosceles triangles. This means triangle EBC is isosceles. In an isosceles triangle, the two base angles are the same. So, angles EBC and BCE are both 61. Now, in a triangle, the three angles add up to 180. So, 61+61=122, and to find angle CEB you need to subtract 180-122. 180-122=58 degrees.
