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Math

Math Snap

PROBLEM

Find the unknown angle measures.

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 180180^\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 \angleB is 62^\circ, and side AC is opposite \angleB, the other two angles must be equal.
Since side AB is opposite \angleC, we know that C=A\angle C = \angle A.
Therefore, \angleC 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 \angleB is 62^\circ and \angleC is 62^\circ.
Let's use this knowledge to find \angleA!

STEP 6

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

STEP 7

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

STEP 8

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

STEP 9

To isolate \angleA, we need to add 124-124^\circ to both sides of the equation:
A+124124=180124 \angle A + 124^\circ - 124^\circ = 180^\circ - 124^\circ A=56 \angle A = 56^\circ

SOLUTION

\angleA = 56\mathbf{56^\circ} and \angleC = 62\mathbf{62^\circ}.
We rocked it!

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