Answer:
4. The smaller angle is 35°.
5. AngleCAB = 40°
AngleDAC = 50°
Explanation:
4) The 3 angles shown all together add up to 180°.
3x+10 + 90° + 2x+5 = 180°
combine like terms.
5x + 105 = 180
subtract 105
5x = 75
divide by 5
x = 15
One of the angles is 3x+10 and the other is 2x+5.
2x+5 is the smaller angle. If x=15, then 2x+5
= 2(15) + 5
= 30 + 5
= 35
The smaller angle is 35°.
5) The two angles in this question add up to 90°.
7x-16 + 6x+2 = 90°
combine like terms
13x - 14 = 90
add 14
13x = 104
divide by 13
x = 8
Angle CAB = 7x - 16
= 7(8) - 16
= 56 - 16
= 40
AngleCAB = 40°
AngleDAC = 6x + 2
= 6(8) + 2
= 48 + 2
= 50
We also could have just subtracted to find angleDAC 90 - 40 = 50.
AngleDAC = 50°