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puteri [66]
3 years ago
7

PLEASE HELP MEEEEEEEEDetermine the internal and external angles of the triangle below​

Mathematics
1 answer:
zloy xaker [14]3 years ago
6 0

Answer:

The internal angles are 78°, 72°, 30°, and the external angle is 150°

Step-by-step explanation:

In a triangle, the measure of an external angle at one vertex equals the sum of the measures of the opposite internal angles to this vertex

In the given figure

∵ The angle of measure (4x + 22) is an exterior angle

∵ The angles of measures (3x - 18) and (2x + 8) are the opposite

   interior angles

→ By using the rule above

∴ (3x - 18) + (2x + 8) = (4x + 22)

→ Add the like terms in the left side

∵ (3x + 2x) + (-18 + 8) = 4x + 22

∴ 5x + (-10) = 4x + 22

→ Remember (+)(-) = (-)

∴ 5x - 10 = 4x + 22

→ Add 10 to both sides

∵ 5x - 10 + 10 = 4x + 22 + 10

∴ 5x = 4x + 32

→ Subtract 4x from both sides

∵ 5x - 4x = 4x - 4x + 32

∴ x = 32

→ Substitute the value of x in the external and internal angles to find them

∵ The external angle = 4(32) + 22 = 128 + 22

∴ The external angle = 150°

∵ One of the internal angle = 3(32) - 18 = 96 - 18

∴ One of the internal angle = 78°

∵ Other internal angle = 2(32) + 8 = 64 + 8

∴ Other internal angle = 72°

→ The sum of the measure of the internal angles of a Δ is 180°

∵ The third internal angle of the triangle = 180° - 78° - 72°

∴ The third internal angle of the triangle = 30°

∴ The internal angles are 78°, 72°, 30°, and the external angle is 150°

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3 years ago
Find the missing angle
GenaCL600 [577]

Step-by-step explanation:

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So,

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6 0
2 years ago
Work out the size of the angle marked x.<br> x<br> 145
dedylja [7]

Answer:

x = 125°

Step-by-step explanation:

The sum of the angles around a point = 360° , then

90 + 145 + x = 360°

235° + x = 360° ( subtract 235° from both sides )

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5 0
2 years ago
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e-lub [12.9K]

Answer:

Step-by-step explanation:

by inspection

angles 2 and 3 are equal, so they will be half angle ABC

angles 1 and 5 are equal  so they will be

      angle 1 + angle 5 + angleABC = 180°      kind of a rule for triangle

                                                                        the sum of all angles - 180°

      (angle 1) x 2 = 180° - 70°

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      angle 1 = 55°   which equals angle 5

angle 4 is clearly a right angle 90°

DO the same procedure for the bottom triangle

angle 8 and 9 are half of angle ADC

angle 8 and 9 are half of 46°

both are 23°

angle 6 equals angle 7

2 ×angle 6 = 180° - 46°

angle 6 = 90° - 23°

angle 6 = 67°    angle 7 = 67°

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2 years ago
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Step-by-step explanation:

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2 years ago
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