Question

The measure of the angle shown on the right is

___°

Answer 1

you need to calculate the angle counter clockwise

you can see that you have essentially a half circle (180°)+the diagonal (45°)=225°
additionally you have 2 lines/circles "underneath" the angle so you know you need to add 2 full circles (360° each):
225+360*2=225+720=945° which should be your solution

Answer 2

To solve the question we will first name the points on the spiral and then divide the angles to measure and then we will add all the angles. The measure of the angle shown is 945°.

We must know,

• A complete circle or revolution is 360°.
• the trigonometric function of tan.

In ΔAPE

$tan (\angle A) = \dfrac{AP}{PE}\\\\ tan (\angle A) = \dfrac{3}{3}\\\\ tan (\angle A) = 1\\\\ (\angle A) = tan^{-1}\ 1\\\\ (\angle A) = 45^o$

Angles

1. ∠QAC, the angle is completing a quarter of the graph, therefore, the angle will be 90°.
2. At the beginning of the spiral, from A to B it will be a complete circle, therefore, the angle will be 360°.
3. From B to C, the spiral will make another circle, therefore, the angle will be 360° again.
4. From C to D, the spiral is completing a quarter of the graph, therefore, the angle will be 90°.
5. From D to E, the spiral will make an angle of 45°.

Sum of All

∠xAE = ∠(QAC) + ∠(A to B) +  ∠( B to C) +  ∠(C to D) +  ∠(D to E)

∠xAE = 45° + 360° + 360° + 90° + 45°

∠xAE = 945°

Hence, the measure of the angle shown is 945°.

Learn more about Trigonometric function:

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