Two base angles of an isosceles triangle measure (3x + 2) and (5x - 30) degrees. How many degrees are in the third angle of the triangle?

Geometry! Nice!

Step-by-step explanation:

This is very simple. In a nutshell, base angles in a isosceles triangle are equal.

Thus:

Time to solve!

Now that we have found the x-value, all we need to do is input it back in for one of the angles.

Moving on, there is a rule in geometry that states that the sum of all angles in triangles is equal to 180, no matter what.

All that has to be done is just multiply 50 by 2, add y in for our third angle, and set that equal to 180.

After all that, the measure of the third angle in the triangle is 80 degrees (make sure to include degrees in your answer).

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i'm not sure i quite understand, could you provide more information?

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°