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Pachacha [2.7K]
2 years ago
10

Two angles of a quadrilateral are of measures 75° and 117° respectively and the other two angles are equal find the measure of e

ach of the equal angles​
Mathematics
1 answer:
insens350 [35]2 years ago
4 0

<u>Answer:</u>

<u>Step-by-step explanation:</u>

The sum of interior angles of a quadrilateral is 360°.

If we consider the measure of one of the unknown angles to be x°, we can set up the following equation:

x + x + 75^\circ + 117^\circ = 360^\circ

Now we can solve for x:

⇒ 2x + 192^\circ = 360^\circ

⇒ 2x = 360^\circ - 192^\circ        [subtracting 192° from both sides]

⇒ 2x = 168^\circ

⇒ x = \frac{168^\circ}{2}                      [dividing both sides by 2]

⇒ x = \bf84^\circ

Therefore, the other two angles each have a measure of 84°.

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Rhombus ABCD has perimeter 148, and one of its diagonals has length 24. How long is the other diagonal?
inn [45]

Answer:

70 units.

Step-by-step explanation:

The 4 sides of a rhombus are equal so each side has length 148 /4

= 37 units. The diagonals bisect each other at right angles so when we draw the 2 diagonals we have 4 congruent right-angled triangles.

So consider one of these triangles:

The hypotenuse is 37 units and one of the legs = 1/2 * 24 = 12 units ( half of the diagonal of length 24).

So the other leg is found using Pythagoras:

x^2 = 37^2 - 12^2 = 1225

x = 35.

This is half of the other diagonal so the latter  = 70 units.

7 0
3 years ago
A line's y-intercept is –9, and its slope is 1/6 .What is its equation in slope-intercept form?
ANEK [815]

Answer:

y = 1/6x - 9

Step-by-step explanation:

The slope-form intercept formula is y = mx + b

4 0
2 years ago
Find a8 of the sequence 10,9.75,9.5,9.25,
borishaifa [10]

Answer:

7.25

Step-by-step explanation:

10,9.75,9.5,9.25,

the rest of the sequence would look like

8, 7.75, 7.5, 7.25, 7, 6.75, 6.5, 6.25, 6 etc.

(the pattern is - .25 from the previous number.

so the 8th number in this sequence is 7.25

hope this helps!!:)

6 0
3 years ago
Read 2 more answers
The angle of elevation from point A to the top of a cliff is 38 degrees. If point A is 80 feet from the base of the cliff, how h
mr Goodwill [35]
The tangent ratio is
   tan(38°) = opposite/adjacent = (height of cliff)/(distance to base)
Multiplying the equation by the denominator gives
   height of cliff = (80 ft)*tan(38°) ≈ 62.5 ft
6 0
3 years ago
Use double angle formulas to find the exact value of sin2x,cos2x, and tan2x
denis-greek [22]
Sin2x = 2sinxcosx;
cos2x = (cosx)^2 - (sinx)^2;
tan2x = (sin2x)/(cos2x);

 cosx = 5/13 from formula (sinx)^2 + (cosx)^2 = 1;

=> sin2x = 120/169; 
.................................

5 0
3 years ago
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