Answer:
2. x = 18
3. x = 7
4. missing angles are 73°
Step-by-step explanation:
The simple rules involved here are ...
- the sum of angles of a triangle is 180°
- angles forming a linear pair are supplementary (total 180°).
Together, these tell you that the external angle of a triangle has the same measure as the sum of the opposite internal angles. (The third angle is the supplement of the external angle.)
<u>Problem 1</u>
Work shown is correct.
__
<u>Problem 2</u>
Using the above observation, ...
(5x -11)° + (2x +20°) = (11x -63)°
7x +9 = 11x -63 . . . . . collect terms, divide by °
72 = 4x . . . . . . . . . . . add 63-7x
18 = x
__
<u>Problem 3</u>
The angles of an equilateral triangle are 60°, so that is the measure of the marked angle.
9x -3 = 60
9x = 63 . . . . . . add 3
x = 7 . . . . . . . . .divide by 9
__
<u>Problem 4</u>
You don't need to find the value of x to answer this question. The base angle of an isosceles triangle is the complement of half the apex angle. This comes from the fact that the two base angles are equal measure.
(apex angle) + 2(base angle) = 180° . . . . sum of angles in isosceles triangle
(1/2)(apex angle) +(base angle) = 90° . . . divide by 2
base angle = 90° -(1/2)(apex angle) . . . . .solve for base angle
Filling in the given apex angle value, we get ...
base angle = 90° -(1/2)(34°) = 73°
Both missing angles are 73°.
