An isosceles triangle has angle measures of (2x degrees) and (5x degrees). What are three possible angle measures of the triangle? Show all work.

Step-by-step explanation:

The interior angles of any triangle always add up to . In an isosceles triangle, (at least) two sides are congruent and therefore their base angles are also congruent. We can then form the following equation:

, where is some constant.

Solving, we get:

Therefore, plugging our constant back in, our angles are:

.

Note this is only one group of possible angles. We could've also set the angle represented by to be the pair of angles that are congruent, and depending on your definition of isosceles, each angle measure could be (equilateral).

4.08%

step-by-step explanation:

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°