Question

in the isosceles triangle $\triangle abc$, $ab = bc$. the measure of $angle a$ is $73^{circ}$, and the measure of $angle b$ is $(6x + 4)^{circ}$. what is the value of $x$?

5
17.2
10
cannot be calculated using given information

Explanation:

Step1: Identify equal angles in isosceles triangle

In isosceles triangle \( \triangle ABC \) with \( AB = BC \), the base angles are \( \angle A \) and \( \angle C \). So \( \angle A=\angle C = 73^\circ \).

Step2: Use triangle angle sum property

The sum of angles in a triangle is \( 180^\circ \). So \( \angle A+\angle B+\angle C = 180^\circ \). Substituting \( \angle A = 73^\circ \), \( \angle C = 73^\circ \), and \( \angle B=(6x + 4)^\circ \), we get \( 73+(6x + 4)+73 = 180 \).

Step3: Simplify the equation

First, combine like terms: \( 6x+4 + 73+73=6x + 150 \). So the equation becomes \( 6x+150 = 180 \).

Step4: Solve for x

Subtract 150 from both sides: \( 6x=180 - 150=30 \). Then divide both sides by 6: \( x=\frac{30}{6}=5 \).

Answer:

\( x = 5 \) (corresponding to option: 5)