Answer:
Step-by-step explanation:
By the triangle sum theorem, the sum of angles in a triangle is equal to 180°. Therefore, m∠A + m∠B + m∠C = 180°. Using the Substitution property
(6x)° + 90° + (x+6)° = 180°
To solve for x, first combine the terms to get (7x + 96) = 180°
Using the Subtraction property of equality,
7x = 84.
Then using the division property of equality x = 12.
To find the measure of angle A,
Use the subtraction property to get m∠A = 6(12)°.
Finally simplifying the expression gets m∠A = 72°.
8 is your range, 15-7= 8.
Let's begin by listing out the information given to us:
We start out by observing that Triangles MKR & ACD are similar or proportional

We will solve for the missing side by using the similar triangle theorem. This is shown below:~
Answer:
<B = 56 degrees
Step-by-step explanation:
The sum of two complementary angle is 90 degrees
Hence <A + <B = 90
2x++18 + 6x + 8 = 90
8x + 26 = 90
8x = 90-26
8x = 64
x = 64/8
x = 8
Get <B
<B = 6x+8
<B = 6(8) + 8
<B = 48+8
<B = 56 degrees
Refer to the attached diagram for help.
All radii of a circle are congruent.
Tangent segs LP and LQ are congruent. (Tangent segs drawn to a circle from the same point are congruent)
Because of this we can establish OPLQ as a kite.
OPLQ is a kite implies that OL bis. angle PLQ.
An angle bis. divides an angle into 2 congruent, parts, so angle OLP must be 30 degrees.
Since tangents form right angles with the radius, angle OPL is right.
Now we have a right triangle OPL with a 30-degree angle. The other angle must be 60 degrees because of the no-choice theorem. (180-(30+90)) = 60
We know that OP is 6 because it is a radius of circle O. How do we use that to find OL? Well, we <em>could</em> use trig, but you might recognize this as a special triangle!
The side opposite the 30 degree angle = x
The side opposite the right angle = 2x
So OL must be 12!