Question

what is the measure of angle x in the image given below ? a.60 b.90 c.120 d.135​

Answer 1

$c. \: 120$

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Answer 2

Given: A geometric figure with the unknown angle x

To find: The measure of angle x

Solution: We know the sum of all the angles of a triangle is equal to 180°.

So according to the question,

In the triangle ABC,

30° + 30° + angle ACB = 180°

⇒ 60° + angle ACB = 180°

⇒ angle ACB = 180° - 60°

⇒ angle ACB = 120°

Hence, we can now calculate angle ACD since it is supplemetary with angle ACB.

∴ angle ACB + angle ACD = 180°

⇒ 120° + angle ACD = 180°

⇒ angle ACD = 180° - 120° = 60°.

According to the question, angle ADC is equal to angle ACD.

Hence, angle ADC = 60°.

In the triangle ACD,

angle ADC + angle ACD + angle CAD = 180°

⇒ 60° + 60° + angle CAD = 180°

⇒ angle CAD = 180° - 120°

⇒ angle CAD = 60°

Now we see the three angles 30°, angle CAD and x on the straight line AB.

Their sum is equal to 180°.

Therefore, 30° + angle CAD + x = 180°

              ⇒ 30° + 60° + x = 180°

              ⇒ 90° + x = 180°

              ⇒ x = 90°

Answer: Option b. 90