Question

If m∠DBC= (12x–3) ° , m∠DBE= (5x +12) ° , and m∠EBC= (3x+ 13) ° , find m∠EBC.

A) 12°
B) 26°
C) 43°
D) 52°

Answer 1

To find the measure of angle EBC, we need to set up an equation using the given information and solve for x. Once we find the value of x, we can substitute it back into the equation to find the measure of angle ABC. The measure of angle EBC is 40.7°.

Step-by-step explanation:

To find the measure of angle EBC, we need to set up an equation using the given information. According to the angle relationships in a triangle, the sum of the angles in a triangle is always 180°. So, we can write the equation:

(12x–3)° + (5x +12)° + (3x+ 13)° = 180°

Combine like terms:

20x + 22 = 180

Subtract 22 from both sides:

20x = 158

Divide by 20:

x = 7.9

Substitute x back into the given angles to find the measure of angle EBC:

m∠EBC = (3(7.9)+ 13)° = 40.7°