Question

In the diagram below of ΔABC , AB ≅ AC , m∠A = 3x , and m∠B = x + 20.
What is the value of x?

Answer 1

Answer on Question # 70897 – Math – Geometry

Question

In the diagram below of $\Delta ABC$, $AB \cong AC$, $m\angle A = 3x$, and $m\angle B = x + 20$. What is the value of $x$?

Solution

The triangle $\Delta ABC$ is shown in the diagram below. If $AB \cong AC$ then $\Delta ABC$ is isosceles with legs $AB$ and $AC$, base $BC$, vertex $A$, vertex angle $A$, and base angles at $B$ and $C$.

Use the theorem: If two sides of a triangle are congruent, $AB \cong AC$, then the angles opposite these sides are also congruent, that is, $\angle C \cong \angle B$. Hence

$$m\angle C = m\angle B = x + 20.$$

Now we use the theorem: In a triangle, the sum of the measures of the interior angles is $180{}^\circ$, that is,

$$m\angle A + m\angle B + m\angle C = 180{}^\circ.$$

Substituting values $m\angle A = 3x$, $m\angle B = m\angle C = x + 20$ we get the equation with respect to $x$:

$$3x + x + 20 + x + 20 = 180$$

Solving this equation

$$\begin{array}{l} 5x + 40 = 180 \\ 5x = 180 - 40 \\ 5x = 140 \\ x = \frac{140}{5} \\ x = 28 \\ \end{array}$$

Answer: $x = 28$.

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