Answer:
Option 4: <u>(2x + 16)° + (x)° = 180°</u>
Step-by-step explanation:
See the attached figure.
For a quadrilateral inscribed in a circle
The opposite angles are supplementary.
So, ∠D + ∠B = 180°
From the figure:
∠B = x° and ∠D = (2x+16)°
∴ <u>(2x + 16)° + (x)° = 180°</u>
Answer:
Part 5.1.1:
Part 5.1.2:
Step-by-step explanation:
We are given that:
Part 5.1.1
Recall that:
Let θ = 2<em>A</em>. Hence:
Square the original equation:
Hence:
Subtract:
Take the square root of both sides:
Since 0° ≤ 2<em>A</em> ≤ 90°, cos(2<em>A</em>) must be positive. Hence:
Part 5.1.2
Recall that:
We can use the third form. Substitute:
Solve for cosine:
In conclusion:
(Note that since 0° ≤ 2<em>A</em> ≤ 90°, 0° ≤ <em>A</em> ≤ 45°. Hence, cos(<em>A</em>) must be positive.)
