Math / Geometry

QuestionFind the unknown angle measures.

Studdy Solution

STEP 1

What is this asking? We need to find the missing angles in this isosceles triangle! Watch out! Don't forget that isosceles triangles have two equal sides and two equal angles.
Also, all angles inside a triangle always add up to $180^\circ$ !

STEP 2

1. Find angle C.
2. Find angle A.

STEP 3

Look closely!
Sides AB and BC are marked with the same single dash.
This tells us they have the same length.
So, triangle ABC is an isosceles triangle.

STEP 4

In isosceles triangles, the angles opposite the equal sides are also equal.
Since $\angle$ B is 62 $^\circ$ , and side AC is opposite $\angle$ B, the other two angles must be equal.
Since side AB is opposite $\angle$ C, we know that $\angle C = \angle A$ .
Therefore, $\angle$ C is also 62 $^\circ$ !
How cool is that?!

STEP 5

We know that the sum of the angles in any triangle is 180 $^\circ$ .
We already know $\angle$ B is 62 $^\circ$ and $\angle$ C is 62 $^\circ$ .
Let's use this knowledge to find $\angle$ A!

STEP 6

We can write this as an equation: $\angle A + \angle B + \angle C = 180^\circ$

STEP 7

Substitute the known values: $\angle A + 62^\circ + 62^\circ = 180^\circ$

STEP 8

Combine the known angles: $\angle A + 124^\circ = 180^\circ$

STEP 9

To isolate $\angle$ A, we need to add $-124^\circ$ to both sides of the equation: $\angle A + 124^\circ - 124^\circ = 180^\circ - 124^\circ$ $\angle A = 56^\circ$

STEP 10

$\angle$ A = $\mathbf{56^\circ}$ and $\angle$ C = $\mathbf{62^\circ}$ .
We rocked it!

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