Answer:
2) x = 41
7) x = 12, Scalene Acute Triangle
Step-by-step explanation:
2 .............................
An isosceles triangle has 2 equal sides, this also means the angles opposite the 2 sides are equal.
76 + 76 + a = 180 ----> a = 28
b + b + m<2 = 180 ---> m<2 = 180 - 2b
a,b form a right angle
a + b = 90
28 + b = 90
b = 62
Sub in to find m<2
m<2 = 180 - 2(62) = 180 - 124 = 56
Finally, use m<2 =56 to solve for x
x + 15 = 56
x = 56 - 15 = 41
7 ................................
BAD and BAC are supplementary angles because they lie on a straight line
BAC = 180 - 122 = 58
Sum of angles in a triangle must equal 180.
(5x+9) + (4x+5) + 58 = 180
Combine like terms and solve for x
9x + 72 = 180
9x = 108
x = 12
Sub in x = 12 back in to find measures of angles.
5(12) + 9 = 69 , 4(12) + 5 = 53
All 3 angles are less than 90 ---> Acute Triangle
All 3 angles are unique implies all sides are different ---> Scalene Triangle
