Question 300·Easy·Math

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In $\triangle ABC$ , the measure of $\angle A$ is equal to the measure of $\angle B$ . If $\angle C$ measures $42^\circ$ , what is the measure of $\angle A$ ?

Two equal angles in a triangle have the same measure. The triangle angle sum says all three interior angles add to $180^\circ$ , so give the equal angles one variable, write an equation, and solve it in Desmos. The measure left after the third angle belongs to both equal angles together, not to either one alone.

Hints

Hint 1
The interior angles are the three angles inside a triangle, and they add to $180^\circ$ . How can you use that total with the given measure of $\angle C$ ?
Hint 2
Give $\angle A$ and $\angle B$ the same variable because their measures are equal. Your equation needs one term for each of those angles, plus the term for $\angle C$ .

Step-by-step

Write the triangle angle equation
Step 1
Translate the angle facts into an equation
Call the measure of each equal angle $x^\circ$ . The interior angles, the angles inside a triangle, add to $180^\circ$ , so:
$x+x+42=180.$
The two $x$ terms represent $\angle A$ and $\angle B$ ; $42$ represents $\angle C$ .
Step 2
Combine the equal-angle terms
Combine the two $x$ terms:
$2x+42=180.$
Here, $2x$ is the sum of both equal angles, not the measure of $\angle A$ alone.
Step 3
Solve for the angle asked for
Type $2x_1+42\sim180$ in Desmos. Use $x_1$ and $\sim$ to tell Desmos to find the value that makes both sides equal. Under PARAMETERS, it gives $x_1=69$ . Since $x$ is the measure of each equal angle, $\angle A$ measures $69^\circ$ . Choice B.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse triangle angle theorems

Question 300·Easy·Math

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