A MultipleChoice 1 Two complementary angles measure 12x 189

A. Multiple-Choice 1. Two complementary angles measure (12x- 18)9 and (Sx+23). What is the measure of the smaller angle? (2) 42 (3) 48 (4) 90° 2. Two supplementary angles measure (7x +11)° and (14x + 1)°. What is the measure of the smaller angle? (1 40.5 (2) 67 (3) 108° (4) 1230 (8-30), (6x + 12) 3. AC and BD intersect at O. If m LDOC \" (8x-30)\" and m

Solution

1. Complementry angles should add up to 90
So, 12x-18+5x+23 = 90
17x=85
x = 5
So, 12x-18 = 42 and 5x+23 = 48 , A
The measure of smaller angle is 42

2. Summplentry angles should to 180
So, 7x+11+14x+1 = 180
21x+12 = 180
x = 8
So, 7x+11 = 67 and 14x+1 = 112
The smallest angle is 67

3. Angles made by same sides are equal. 8x-30 = 6x+12, so, 2x = 42, x=21
And DOA +8x-30 = 180
DOA + 8*21-30 = 180
DOA = 180-138 = 42
DOA = 42

4. The value of x=?
All angles should sum to 360
x+98+48+117 = 360
x=97