Angles of Triangles (includes Isosceles & Equilateral) Scavenger ... - Free Printable

Let’s solve the problem step by step.

We are told that triangle CDE is isosceles. That means two of its sides are equal — and in this case, we can see from the tick marks on the diagram that side CD equals side DE. So, the angles opposite those sides must also be equal.

That means:
- Angle at C (which is labeled as (8x + 17)°)
- Angle at E (which is labeled as (8x - 13)°)

Wait — hold on! If CD = DE, then the angles opposite them should be equal. Let’s double-check which angles are opposite which sides.

In triangle CDE:
- Side CD is opposite angle E
- Side DE is opposite angle C
- Side CE is opposite angle D

So if CD = DE, then angle E = angle C.

But looking at the labels:
- Angle C = (8x + 17)°
- Angle E = (8x - 13)°

If they’re supposed to be equal, then:

> 8x + 17 = 8x - 13

Subtract 8x from both sides:

> 17 = -13 → That’s not possible!

Hmm… that can’t be right. Maybe I misread which sides are equal.

Looking again at the diagram: The tick marks are on sides CD and CE, not CD and DE.

Wait — let me look carefully.

Actually, in the image, the tick marks are on side CD and side CE — meaning those two sides are equal. So triangle CDE has CD = CE.

Therefore, the angles opposite those sides are equal.

- Side CD is opposite angle E
- Side CE is opposite angle D

So if CD = CE, then angle E = angle D.

Angle E is given as (8x - 13)°
Angle D is what we’re trying to find — but it’s not directly given. Wait — actually, angle D is the vertex angle, and angles at C and E are the base angles? No — let’s label properly.

Triangle CDE:
- Vertices: C, D, E
- Sides: CD, DE, EC
- Angles: ∠C, D, ∠E

Given: CD = CE → so sides from C to D and C to E are equal → so triangle is isosceles with apex at C.

Therefore, the two equal angles are the ones at D and E.

Yes! Because in an isosceles triangle, the angles opposite the equal sides are equal.

Since CD = CE, then:

→ Angle opposite CD is angle E
→ Angle opposite CE is angle D

So angle D = angle E

Perfect.

So:

∠D = ∠E = (8x - 13)°

And ∠C = (8x + 17)°

Now, sum of angles in any triangle is 180°.

So:

∠C + D + ∠E = 180°

Plug in:

(8x + 17) + (8x - 13) + (8x - 13) = 180

Combine like terms:

8x + 8x + 8x = 24x
17 - 13 - 13 = 17 - 26 = -9

So:

24x - 9 = 180

Add 9 to both sides:

24x = 189

Divide by 24:

x = 189 ÷ 24

Let’s simplify that fraction.

Both divisible by 3:

189 ÷ 3 = 63
24 ÷ 3 = 8

So x = 63/8 = 7.875

But maybe we don’t need decimal — let’s keep it as fraction for accuracy.

x = 63/8

Now, we want to find measure of ∠D, which is (8x - 13)°

Plug in x = 63/8:

8 * (63/8) = 63

Then 63 - 13 = 50

So ∠D = 50°

Let’s verify:

∠C = 8x + 17 = 8*(63/8) + 17 = 63 + 17 = 80°
∠D = 50°
∠E = 50°

Sum: 80 + 50 + 50 = 180° → Correct!

Also, since CD = CE, angles opposite them (∠E and ∠D) are equal → 50° each → makes sense.

Final Answer:
50°