Question

Hi there ms or mr could you please help me with this problem? oh no this isn't a test it's practice work from my teacher it's my first time in geometry so i might get concept of somethings that your doing and i might get stuck too

Answer 1

The diagram shows an isosceles triangle. An isosceles triangle has two sides equal in measurement, and the two corresponding angles are also equal. With this we can identify all three angles (even though only two were identified in the question.

Line AB is congruent to line BC as stated. That makes angle A equal to angle C. If angle A is x, then angle C is also x (rule of isosceles triangle). Remember also that angles in a triangle sum up to 180 degrees, which means that angle A plus angle B plus angle C all equals 180.

Therefore;

`\begin{gathered} \text{If A+B+C=180, then;} \\ x+(x+30)+x=180 \\ x+x+30+x=180 \\ 3x+30=180 \\ \text{Subtract 30 from both sides of the equation;} \\ 3x+30-30=180-30 \\ 3x=150 \\ \text{Divide both sides by 3, and you have} \\ (3x)/(3)=(150)/(3) \\ x=50 \end{gathered}`