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2 years ago

Find the value of x

Mathematics

2 answers:

Karo-lina-s [1.5K]2 years ago

7 0

Answer:

x = 68°

Step-by-step explanation:

∠ DCB = ∠ EDC = 27° ( alternate angles )

Thus ∠ ECB = 23° + 27° = 50°

The sum of the 3 angles in a triangle = 180°, thus

x = 180° - (62 + 50)° = 180° - 112° = 68°

kvv77 [185]2 years ago

4 0

Answer:

68°

Step-by-step explanation:

DE ║ BC

So, ∠DBC = ∠ADE = 62° (∵ Corresponding Angles are equal )

In triangle DEC ,

∠EDC+ ∠ECD = ∠AED (∵ Exterior Angle Sum Property of a triangle )

⇒ ∠AED = 23° + 27° = 50°

Now in triangle AED ,

∠EAD + ∠ADE + ∠AED = 180°

⇒ x° + 62° + 50° = 180°

⇒x° = 180° - 112° = 68°

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step 1

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x ---> the measure of the interior angle

y ---> the measure of the exterior angle

Remember that

the sum of the interior and exterior angle in any polygon is equal to 180 degrees

$x+y=180^o$ ----> equation A