Answer:
Step-by-step explanation:
From the picture attached,
∠4 = 45°, ∠5 = 135° and ∠10 = ∠11
Part A
∠1 = ∠4 = 45° [Vertically opposite angles]
∠1 + ∠3 = 180° [Linear pair of angles]
∠3 = 180° - ∠1
= 180° - 45°
= 135°
∠2 = ∠3 = 135° [Vertically opposite angles]
∠8 = ∠5 = 135° [Vertically opposite angles]
∠5 + ∠6 = 180° [Linear pair of angles]
∠6 = 180° - 135°
∠6 = 45°
∠7 = ∠6 = 45° [Vertically opposite angles]
By triangle sum theorem,
m∠4 + m∠7 + m∠10 = 180°
45° + 45° + m∠10 = 180°
m∠10 = 180° - 90°
m∠10 = 90°
m∠10 = m∠12 = 90° [Vertically opposite angles]
m∠10 = m∠11 = 90° [Given]
Part B
1). ∠1 ≅ ∠4 [Vertically opposite angles]
2). ∠7 + ∠5 = 180° [Linear pair]
3). ∠9 + ∠10 = 180° [Linear pair]
Answer:
3 < x < 27
Step-by-step explanation:
We can't tell what "must ne greater" means, so we'll tell you the limits on the side length and you can choose the one that is relevant.
The third side of a triangle must have a length that lies between the difference and sum of the two lengths you know.
15 -12 = 3
15 +12 = 27
The value of x must be between 3 and 27:
3 < x < 27
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If you allow the triangle to have zero area, then x can be 3 or 27. Many authors claim such a "triangle" is not allowed, so don't allow those cases.
We have point

, so first calculate

. There will be:

Now, we can write the equation of the normal line as:

Normal line (and every line) crosses x-axis when y = 0, so coordinates of A: