Question

Please help ! Find the value of x

Answer 1

hola!

In the given fig. we can observe that:
∠ DAB and ∠ CAB forms a Linear Pair

i.e. ∠ DAB + ∠ CAB = 180°

105° + ∠ CAB = 180°

∠ CAB = 180° - 105°

∠ CAB = 75° ------------(i)

Now, In Triangle ABC

Here,
∠ ABC = x°
∠ BAC = 75° -----[ from eqn. (i) ]
∠ BCA = 67°

by using angle sum property of triangle:

∠ ABC + ∠ BAC + ∠ BCA = 180°

x° + 75° + 67° = 180°

x° + 142° = 180°

x° = 180° - 142°

x° = 38°

Hence, x = 38°

Thus,
Option [ B ] : 38° is Correct

hope it helps!

Answer 2

The measure of angle x will be 38° so option (B) will be correct.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right angle triangle, equilateral triangle, and much more.

In any triangle sum of all interior angles is 180°

Let's say the interior angle at A is y

Then,

x + y + 67 = 180 ⇒ x + 67 = 180 - y

Now,

The angle above a straight line is 180° so

y + 105 = 180 ⇒ y = 75°

So,

(x + 67 ) = 180 - 75

(x + 67° ) = 105°

x = 38°

Hence"The measure of angle x will be 38° ".

For more about triangles,

https://brainly.com/question/2773823

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