Answer:
m∠a = 133°
m∠b = 17°
m∠c = 30°
Explanation:
Step 1: Find x using the Triangle Sum Theorem:
- The Triangle Sum Theorem says that the sum of a triangle's interior angles is 180°.
Thus, we can find x by setting the sum of the angles equal to 180
m∠a + m∠b + m∠c = 180°
(40x - 27) + (25 - 2x) + (26 + x) = 180
(40x - 2x + x) + (-27 + 25 + 26) = 180
(39x + 24 = 180) - 24
(39x = 156) / 39
x = 4
Thus, x = 4.
Step 2: Find m∠a:
First, we can find m∠a by plugging in 4 for x in (40x - 27) and simplifying:
m∠a = 40(4) - 27
m∠a = 160 - 27
m∠a = 133
Thus, m∠a = 133°.
Step 3: Find m∠b:
Now we can find m∠b by plugging in 4 for x in (25 - 2x) and simplifying:
m∠b = 25 - 2(4)
m∠b = 25 - 8
m∠b = 17
Thus, m∠b = 17°.
Step 4: Find m∠c:
Finally, we can find m∠c by plugging in 4 for x in (26 + x) and simplifying:
m∠c = 26 + 4
m∠c = 30
Thus, m∠c = 30°.