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Glencoe Math: Course 3, Volume 2

GM

Glencoe Math: Course 3, Volume 2 View details

3. Angles of Triangles

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Exercise 4 Page 392

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

$31$

Practice makes perfect

We want to find the value of $x$ in the given triangle.

A triangle with an exterior angle measuring 123 degrees is shown. The corresponding remote interior angles are given as 92 and x degrees.

To do so, we will first recall a key piece of information!

Exterior Angles of a Triangle
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.

With this rule, we can write an equation in terms of

x .

123^{\circ} = 92^{\circ} + x^{\circ}

Now, we can solve this equation for

x .

For simplicity, we will not include the degree symbol.

123 = 92 + x

▼

Solve for

x

$LHS - 92 = RHS - 92$

31 = x

Rearrange equation

x = 31

The measure of the missing angle is

3 1^{\circ} .

A triangle is displayed with an exterior angle measuring 123 degrees, and its corresponding remote interior angles are 92 and 31 degrees.

Subchapter links

Guided Practice p.392

Independent Practice p.393-394

H.O.T. Problems p.394

Standardized Test Practice p.394-396

Extra Practice p.395

Common Core Review p.396