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Math  /  Geometry

QuestionFind the measure of the missing angle.
Answer Attempt 1 out of 2 a=a= □\square - Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the measure of an **angle** next to another **angle** that measures 65∘\text{65}^\circ, and they're both on a straight line. Watch out! Don't forget that angles on a straight line add up to 180∘\text{180}^\circ!

STEP 2

1. Set up the equation
2. Solve for *a*

STEP 3

Alright, so we know that the two angles together make a straight line.
A straight line is always 180∘\text{180}^\circ!
That's our **key** here.

STEP 4

We've got one angle that's 65∘ \text{65}^\circ and the other angle is *a*.
Since they make a straight line together, we can write this super simple equation: 65∘+a=180∘ \text{65}^\circ + a = \text{180}^\circ

STEP 5

Now, let's **isolate** *a*!
We want to get *a* all by itself on one side of the equation.
To do that, we need to move that 65∘\text{65}^\circ to the other side.

STEP 6

Since the 65∘\text{65}^\circ is being *added* to *a*, we'll do the *opposite* operation to move it.
The opposite of addition is subtraction!
So, we'll subtract 65∘\text{65}^\circ from *both* sides of the equation: 65∘+a−65∘=180∘−65∘ \text{65}^\circ + a - \text{65}^\circ = \text{180}^\circ - \text{65}^\circ

STEP 7

On the left side, 65∘−65∘\text{65}^\circ - \text{65}^\circ adds to zero, leaving just *a*.
Perfect! On the right side, 180∘−65∘\text{180}^\circ - \text{65}^\circ is 115∘\text{115}^\circ.
So, our equation now looks like this: a=115∘ a = \text{115}^\circ

STEP 8

The missing angle, *a*, measures 115∘\text{115}^\circ.

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