Homework 1:Pythagorean Theorem and it’s Converse

Find The Value of X

x = 14

Step-by-step explanation:

Inside the trapezoid, there are two right triangles, with a hypotenuse of 19 and a leg of 17. The other leg can be computed with the help of the pythagorean theorem as follows:

Now, we can calculate the value of x, as follow;

8.5 + x + 8.5 = 31

17 + x = 31

x = 31 - 17

x = 14

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°