In triangle ABC, the measure of angle A is 25° and the measure of

In triangle $ABC$, the measure of angle $A$ is $25°$ and the measure of angle $B$ is greater than $90°$. Which of the following could be the measure of angle $C$ ?

Indicate all such measures.

  1. $12°$
  2. $15°$
  3. $45°$
  4. $50°$
  5. $70°$

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 10 of Section 6 of Practice Test 1. Those questions testing our knowledge of Triangles can be kind of tricky, but never fear, PrepScholar has got your back!

Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on your paper.

This question wants us to find possible values for an angle within a triangle, so we know that we will use our knowledge of Triangles here. Let’s keep what we’ve learned about this skill at the tip of our minds as we approach this question.

What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

 

  1. We have a triangle with $∠A, ∠B, \and ∠C$
  2. We know $∠A$
  3. We’re given an inequality for $∠B$
  4. We want to know possible values for $∠C$

 

Develop a Plan

Let’s start with a top-down approach, where we will begin with what we’re looking for and work down to the details of what we’re given in this question. We want to know possible values of $∠C$, so let’s think about what we know about $∠C$. We see that it’s in a triangle and we’re given information about the other two angles in that triangle, so let’s think about what math relationship we know that can connect these three angles. Ah, we know that the sum of the angles in a triangle is $180°$:

$$∠A + ∠B + ∠C = 180°$$

We also know that $∠A=25°$ and $∠B > 90°$, so let’s combine these two equations and one inequality to find the possible values for $∠C$.

Solve the Question

We know that when combining equations and an inequality, it is usually easier to start with the inequality and substitute in the equations. So let’s start with our inequality:

$$∠B > 90°$$

We want to combine this inequality with our equation, so let’s solve our equation for $∠B$:

$$∠B = 180° – ∠A – ∠C$$

Substituting the right side of this equation for $∠B$ in our inequality we get:

$$180° – ∠A – ∠C > 90°$$

We know that $∠A=25°$, so let’s plug that in now:

$$180° – 25° – ∠C > 90$$

Now let’s simplify this and solve for $∠C$, remembering that we need to switch the direction of inequality symbols whenever we multiply or divide by negative numbers:

$180° – 25° – ∠C$ $>$ $90°$
$155° – ∠C$ $>$ $90°$
$- ∠C$ $>$ $-65°$
$∠C$ $<$ $65°$

Excellent. So we know that $∠C$ must be less than $65°$, so the correct answer is A, B, C, and D.

What Did We Learn

When combining an equation with an inequality, it should be easier to start with the inequality and then use the equation to substitute for variables.

 

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