Answer:
The answer is angle 7, 3, and 2
Step-by-step explanation:
Angle 7 is vertical, angle 3 is alternate exterior, and angle 2 is corresponding.
The value of 'x' is 24.2 and the value of 'y' is 46.5.
To solve this, we do the following steps.
<u>Step 1:</u> Divide 'y' into 2 parts, 'a' and 'b'. 'a' would be the lower leg of the 45°-45°-90° triangle, while 'b' is the lower leg of the 30°-60°-90° triangle.<em>
</em><u>Step 2:</u> Given the hypotenuse (34) of the 30°-60°-90° triangle, solve for 'b' using the cosine of 30°.
cos30° = b/34 [adjacent over hypotenuse]
b = 34cos30° [cross-multiply]
b = 29.4
<u>Step 3:</u> Solve for the 90° leg (the side opposite the 30° angle) using the Pythagorean Theorem. We will name this leg "h" (cuz height).
l² + l² = hyp²
29.4² + h² = 34²
h² = 1156 - 864.36
√h² = √291.64
h = 17.1
<u>Step 4:</u> Solve for 'x' by using the 45°-45°-90° triangle ratio (1:1:√2). √2 would be the hypotenuse of the 45°-45°-90° triangle, while 1 would be both congruent legs.
Side 'h' is one of the legs; side 'a' is the other. Since these legs are congruent, 'a' also measures 17.1. Now all we need to do is solve for 'x', which is our hypotenuse. To do this, we simply multiply the measure of side 'h' or 'a' by √2.
x = 17.1 × √2
x = 24.2
<u>Step 5:</u> Now that we got the value of 'x', solve for 'y' by adding the measures of sides 'a' and 'b' together.<em>
</em><u /> y = a + b
y = 17.1 + 29.4
y = 46.5
And there you have it! <em>Hope this helps.</em>
<em>
</em>
2(x-6)=3(x+3)
Let's solve your equation step-by-step.
<span><span>2<span>(<span>x−6</span>)</span></span>=<span>3<span>(<span>x+3</span>)
</span></span></span>Step 1: Simplify both sides of the equation.
<span><span>2<span>(<span>x−6</span>)</span></span>=<span>3<span>(<span>x+3</span>)
</span></span></span><span>Simplify: (Show steps)
</span><span><span><span>2x</span>−12</span>=<span><span>3x</span>+9
</span></span>Step 2: Subtract 3x from both sides.
<span><span><span><span>2x</span>−12</span>−<span>3x</span></span>=<span><span><span>3x</span>+9</span>−<span>3x
</span></span></span><span><span><span>−x</span>−12</span>=9
</span>Step 3: Add 12 to both sides.
<span><span><span><span>−x</span>−12</span>+12</span>=<span>9+12
</span></span><span><span>−x</span>=21
</span>Step 4: Divide both sides by -1.
<span><span><span>−x/</span><span>−1</span></span>=<span>21/<span>−1
</span></span></span><span>x=<span>−21
</span></span>Answer:
<span>x=<span>−<span>21</span></span></span>
Answer:
Option (4)
Step-by-step explanation:
If two chords intersect outside the circle, angle formed between the chords will be half of the sum of measures of intercepted arcs.
From the given picture,
95° = 
190 = 135 + 
= 55°
Therefore, option (4) will be the correct option.
