The value of x is 32, m∠A = 115° and m∠C = 50°.
Solution:
Given ABC is a triangle.
m∠A = (4x - 13)°, m∠B = 15° and m∠C = (x + 18)°
Sum of the angles of a triangle = 180°
m∠A + m∠B + m∠C = 180°
⇒ (4x - 13)° + 15° + (x + 18)° = 180°
⇒ 4x° - 13° + 15° + x° + 18° = 180°
⇒ 5x° + 20° = 180°
Subtract 20° from both sides.
⇒ 5x° = 160°
Divide by 5 on both sides.
⇒ x° = 32°
⇒ x = 32
m∠A = (4x - 13)°
= (4(32) - 13)°
m∠A = 115°
m∠C = (x + 18)°
= (32 + 18)°
m∠C = 50°
Hence the value of x is 32, m∠A = 115° and m∠C = 50°.
