Question

Segment AB is the diameter of a circle. C is the point on the circumference such that in $\Delta ABC$, $\angle B$ is less by ${10}^{\circ }$ than $\angle A$. Find the measures of all the angles of $\Delta ABC$.

• A. $\angle A={55}^o,\angle B={45}^o,\angle C={80}^o$
• B. $\angle A={40}^o,\angle B={50}^o,\angle C={90}^o$
• C. $\angle A={50}^o,\angle B={40}^o,\angle C={90}^o$
• D. Cannot be determined.

Answer 1

The correct option is C $\angle A={50}^o,\angle B={40}^o,\angle C={90}^o$

$Sinceweareusingtwovariables:Letoneangle=Aandtheotherangle=BThethirdangleC={90}^{\circ },\left(anglemadefromanyptoncircumferencetothediameter\right)SoA+B+90=180(anglesinatraingle=180)B=A-10SoA+A-10+90=1802A=100A=50B=40$