Answer:
∠P = 39º
∠Q=120º
∠R = 21º
Step-by-step explanation:
m∠P+m∠Q+m∠R=180º (sum of ∠s in a triangle)
2x-3+6x-6+x=180º (substitution)
9x-9=180º (algebra)
9x=189º (algebra)
x=21º (algebra) (this is ∠R)
(2x-3)=39º (algebra) (this is ∠P)
6x-6=120º (algebra) (this is ∠Q)
Answer:
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Answer:
7.5
Step-by-step explanation:
Answer:
XQ = 12
Step-by-step explanation:
In this question it asks for XQ instead of x, but you need to find x first.
1. Find x.
XQ is half of MQ so this statement is true: 3x - 3 = 2(2x - 6)
Solve for x.
3x - 3 = 2(2x - 6)
Distribute 2.
3x - 3 = 4x - 12
Isolate x.
3x = 4x - 9
-x = -9
Divide -1 out.
x = 9
Now solve for XQ, which the equation is given.
XQ = 2(9) - 6
XQ = 18 - 6
XQ = 12
He should use the Pythagorean Theorem to find the missing length.
Since KT is tangent to the circle and TL reaches the center of circle L, the measure of angle LTK is 90 degrees. This means that triangle LTK is a right triangle which means the Pythagorean Theorem can be used.
So,
TL²+(12)²=(13)²
=> TL²+144=169
=> TL²=25
=> TL = 5
Therefore, the radius of circle L is 5 feet.