Answer:
60
Step-by-step explanation:
p = 180 - [ 360 - ( 130 + 110 ) ]
= 180 - [ 360 - 240 ]
= 180 - 120
p = 60
- Two angles that are complements of each other add to equal 90 degrees (they are complementary angles).
- One angle measures x degrees.
- The other angle measures 25 more than 4 times the angle that measures x degrees; it measures 4x + 25 degrees.
To find x, set the sum of these expressions (x and 4x + 25) equal to 90 and solve algebraically for x.
90 = x + (4x + 25)
90 = x + 4x + 25
90 = 5x + 25
65 = 5x
13 = x
If you wanted to find the measure of angle x, you'd substitute 13 for x in its expression, 4x + 25.
4x + 25
4(13) + 25
52 + 25
77
Answer:
x = 13
m∠x = 77°
Answer:
r ≤ -5 and r ≥ 1
Step-by-step explanation:
The solution has two parts:
1) that derived from | 2 +r | ≥ 3 when (2 + r) is already positive. Then:
2 + r ≥ 3, or r ≥ 1
and
that derived from | 2 +r | ≥ 3 when (2 + r) is negative. If (2 + r) is negative, then
|(2 + r)| = -(2 + r) = -2 -r, which is ≥ 3. Therefore, -2 -r ≥ 3, or -r ≥ 5. To solve this for r, divide both sides by -1 and reverse the direction of the inequality sign: r ≤ -5
