Question

ANSWER FAST
The measures of the angles of △ABC are given by the expressions in the table.


Angle Measure

A ​​ (12x+12)∘

B 15°

C (3x+18)∘

What is the measure of ∠A and ∠C ?




Enter your answers in the boxes.


​ m∠A= ​ º


​ m∠C= ​ º

Answer 1

∠A + ∠B + ∠C = 180°   (angle sum property)

12x +12° + 15° + 3x + 18° = 180°

15x + 45° = 180°

15x = 180° -  45°

15x = 135°

x = 135°/15

x = 9°

∴ ∠A = (12 × 9 + 12) = 120°

∴ ∠C = (3 × 9 + 18) = 45°

Answer 2

(12x+12)+15+(3x+18)=180°
12x+12+15+13x+18=180
12x+13x+12+15+18=180
25x+55=180
25x=180-55
25x=125
x=125/25
x=5. ........

m(angle A)=(12x+12)
=12(5)+12
=60+12
m(angle A)=72°

m(angle C)=(3x+18)
=3(5)+18
=15+18
m(angle C)=33°