Question

properties of isosceles triangles
score: 0/3 penalty: none
question
in △cde, (overline{de}congoverline{cd}) and (mangle d = 29^{circ}). find (mangle c).
answer

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle $\triangle CDE$ with $DE\cong CD$, $\angle E=\angle C$.

Step2: Use angle - sum property of a triangle

The sum of interior angles of a triangle is $180^{\circ}$. So, $\angle C+\angle D+\angle E = 180^{\circ}$. Since $\angle E=\angle C$, we can rewrite it as $2\angle C+\angle D=180^{\circ}$.

Step3: Substitute the value of $\angle D$

Given $\angle D = 29^{\circ}$, then $2\angle C+29^{\circ}=180^{\circ}$.

Step4: Solve for $\angle C$

First, subtract $29^{\circ}$ from both sides: $2\angle C=180^{\circ}- 29^{\circ}=151^{\circ}$. Then divide both sides by 2: $\angle C=\frac{151^{\circ}}{2}=75.5^{\circ}$.

Answer:

$75.5^{\circ}$