In triangle \$ABC\$, the measure of edge \$A\$ is \$25°\$ and also the measure of angle \$B\$ is better than \$90°\$. I m sorry of the following can be the measure up of edge \$C\$ ?

Indicate every such measures.

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\$12°\$\$15°\$\$45°\$\$50°\$\$70°\$

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## Survey the Question

Let’s search the difficulty for clues regarding what it will certainly be testing, together this will help transition our minds to think around what form of math knowledge we’ll use to settle this question. Pay attention to any type of words that sound math-specific and also anything special about what the number look like, and also mark castle on her paper.

This concern wants us to find possible values because that an angle within a triangle, for this reason we understand that we will use our expertise of Triangles here. Let’s save what we’ve learned around this ability at the reminder of our minds together we technique this question.

## What execute We Know?

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

We have actually a triangle with \$∠A, ∠B, and ∠C\$We know \$∠A\$We’re provided an inequality for \$∠B\$We desire to know feasible values because that \$∠C\$

## Develop a Plan

Let’s begin with a top-down approach, whereby we will begin with what we’re looking for and work down to the details that what we’re offered in this question. We desire to know possible values of \$∠C\$, for this reason let’s think about what we know around \$∠C\$. We check out that it’s in a triangle and also we’re given information around the other two angle in that triangle, so let’s think about what math connection we recognize that can attach these three angles. Ah, we recognize that the sum that the angles in a triangle is \$180°\$:

\$\$∠A + ∠B + ∠C = 180°\$\$

We likewise know the \$∠A=25°\$ and \$∠B > 90°\$, therefore let’s integrate 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 begin with the inequality and also substitute in the equations. Therefore let’s start with ours inequality:

\$\$∠B > 90°\$\$

We want to combine this inequality v our equation, for this reason let’s deal with our equation because that \$∠B\$:

\$\$∠B = 180° – ∠A – ∠C\$\$

Substituting the best side the this equation for \$∠B\$ in our inequality us get:

\$\$180° – ∠A – ∠C > 90°\$\$

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

\$\$180° – 25° – ∠C > 90\$\$

Now let’s simplify this and also solve because that \$∠C\$, remembering the we have to switch the direction the inequality symbols whenever we multiply or division by negative numbers:

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

Excellent. For this reason we understand that \$∠C\$ must be less than \$65°\$, so the exactly answer is A, B, C, and also D.

## What Did we Learn

When combine an equation with an inequality, it should be easier to start with the inequality and also then use the equation come substitute because that variables.

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