Question 348·Easy·Math

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In $\triangle ABC$ , $\angle A$ and $\angle B$ are congruent, and $\angle C$ measures $72^{\circ}$ . What is the measure, in degrees, of $\angle A$ ?

The cue for a triangle angle sum problem is a triangle with one angle known and two related angles. Congruent angles have equal measures, so give them the same variable and add all three angles to $180^\circ$ . Use a Desmos regression to find the variable. Don't treat the known third angle as part of the equal pair.

Hints

Hint 1
Congruent angles have identical measures. Give $\angle A$ one variable, and use that same variable for $\angle B$ , not for the given $\angle C$ .
Hint 2
The interior angles of a triangle add to $180^\circ$ . What equation adds the two equal angles and the $72^\circ$ angle?

Step-by-step

Use the triangle angle sum
Step 1
Name the equal angles
Call the measure of $\angle A$ $x^\circ$ . Congruent means equal in measure, so $\angle B$ also measures $x^\circ$ . $\angle C$ is not part of that equal pair.
Step 2
Write the angle-sum equation
A triangle’s three interior angles, the angles inside it, add to $180^\circ$ . Add the two angles named $x$ and the given $72^\circ$ angle: $x+x+72=180$ . Only the two congruent angles split what remains after the third angle.
Step 3
Find the measure of angle A
Type $x_1+x_1+72\sim180$ in Desmos. Use $x_1$ for the unknown angle measure and $\sim$ in place of $=$ to ask Desmos to find it. Under PARAMETERS, Desmos shows $x_1=54$ . Since $x$ names $\angle A$ , its measure is $54^\circ$ . Choice B.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse triangle angle theorems

Question 348·Easy·Math

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