Question

Please help!!!

What is the measure of ∠X
Angles are not necessarily drawn to scale.

Answer 1

• 
  `\boxed{\mathrm{\angle x = 75^o}}`

Explanation:

Interior angles of a triangle always add up to 180, which means that...

`\mathrm{\angle BDH + \angle DBH + \angle DHB = 180^o}`

From the given the diagram:-

∠BDH = 39°

∠DBH = 36°

Therefore,

`\mathrm{39^o+36^o+\angle DHB=180^o}`

`\boxed{\mathrm{\angle DHB =105^o}}`

∠x and ∠DHB form a straight line meaning they are supplementary angles (They add up to 180°).

`\mathrm{\angle DHB+\angle x=180^o}`

`\mathrm{105 + \angle x=180^o}`

`\mathrm{\angle x = 75^o}`

Therefore, angle x equals 75°.

____________________

Hope this helps!

Answer 2

The measure of ∠x is 75°.

Explanation:

From inspection of the given diagram, triangle BDH is formed by line segments BD, DH and HB. (Shown in red on the attached diagram).

We have been given two of the three interior angles of triangle BDH:

• m∠B = 36°
• m∠D = 39°

Line segment BE is a straight line. As the interior angles of a triangle sum to 180°, and angles on a straight line sum to 180°, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

Angle x is the exterior angle of triangle BDH where angles B and D are the two non-adjacent interior angles. Therefore, x is equal to the sum of angles B and D:

⇒ x = m∠B + m∠D

⇒ x = 36° + 39°

⇒ x = 75°