In , the measure of is equal to the measure of . If measures , what is the measure of ?

Solution available with step-by-step explanation

SAT Lines, Angles & Triangles Question 25 | Free SAT Prep | Aniko

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Question 25·Easy·Lines, Angles, and Triangles

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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 $\angle A$ ?

For triangle angle problems where two angles are equal, immediately use the triangle angle-sum rule ( $\text{sum} = 180^\circ$ ) and represent the equal angles with the same variable, such as $x$ . Write an equation like $x + x + \text{(third angle)} = 180$ , simplify to solve for $x$ , and finally match your result to the answer choices. Always double-check by adding all three angles to confirm they total $180^\circ$ before moving on.

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Recall a key triangle fact

What is the sum of the measures of the three interior angles in any triangle?

Represent the equal angles with a variable

Since $\angle A$ and $\angle B$ are equal, try letting both of them be $x$ . Then write an equation involving $x$ , $x$ , and $42$ .

Set up and solve the angle-sum equation

Use $x + x + 42 = 180$ and solve this equation step by step to find $x$ , which is the measure of $\angle A$ .

Check that your answer is reasonable

After you find $x$ , add $x + x + 42$ and make sure it equals $180$ . If it doesn’t, recheck your arithmetic.

Desmos Guide

Enter the expression for the equal angles

In a new line, type (180 - 42) / 2 to represent subtracting the third angle from $180^\circ$ and then dividing the remaining sum equally between $\angle A$ and $\angle B$ .

Read the calculator output

Look at the value Desmos gives for (180 - 42) / 2; that number (in degrees) is the measure of $\angle A$ . Then choose the answer choice that matches this value.

Step-by-step Explanation

Use the fact that two angles are equal

We are told that $\angle A$ is equal to $\angle B$ . In geometry, when two angles in a triangle are equal, we often let them both be the same variable.

Let $\angle A = x$ and $\angle B = x$ .

Apply the triangle angle sum

In any triangle, the three interior angles always add up to $180^\circ$ .

So for $\triangle ABC$ :

\angle A + \angle B + \angle C = 180^\circ

Substitute $\angle A = x$ , $\angle B = x$ , and $\angle C = 42^\circ$ :

x + x + 42 = 180

Combine like terms:

2x + 42 = 180

Solve the equation for x

Now solve $2x + 42 = 180$ step by step:

Subtract $42$ from both sides:

2x = 180 - 42 = 138

Divide both sides by $2$ :

x = \frac{138}{2} = 69

Since $x$ represents $\angle A$ , the measure of $\angle A$ is $69^\circ$ .

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Step-by-step Explanation

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Step-by-step Explanation