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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

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