Math  /  Geometry

QuestionREL-11. A large triangular piece of plywood is to be painted to look like a mountain for the spring musical. The angles at the base of the plywood measure 7676^{\circ} and 4545^{\circ}. What is the measure of the top angle that represents the mountain peak?

Studdy Solution

STEP 1

What is this asking? We need to find the angle at the top of a triangle, given the other two angles at the bottom. Watch out! Remember that all the angles inside a triangle *always* add up to 180180^\circ.
Don't forget your protractor principles!

STEP 2

1. Sum of Angles
2. Find the Missing Angle

STEP 3

We know that the angles in *any* triangle add up to 180180^\circ.
This is a fundamental fact about triangles!
Let's call the angles at the base A=76\angle A = 76^\circ and B=45\angle B = 45^\circ.
We'll call the unknown angle at the top C\angle C.
So, we can write this relationship as: A+B+C=180 \angle A + \angle B + \angle C = 180^\circ

STEP 4

Let's plug in what we know!
We have A=76\angle A = 76^\circ and B=45\angle B = 45^\circ, so: 76+45+C=180 76^\circ + 45^\circ + \angle C = 180^\circ

STEP 5

Alright, let's **combine** those known angles: 121+C=180 121^\circ + \angle C = 180^\circ We're *so* close to finding that mountain peak angle!

STEP 6

To **isolate** C\angle C, we need to subtract 121121^\circ from *both* sides of the equation.
Remember, what we do to one side, we *must* do to the other!
This keeps everything balanced. 121121+C=180121 121^\circ - 121^\circ + \angle C = 180^\circ - 121^\circ C=59 \angle C = 59^\circ

STEP 7

The measure of the top angle, our majestic mountain peak, is C=59\angle C = 59^\circ!

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