Triangles q r p and x y z are congruent. angle p q r is 72 degrees. the lengths of sides a p and p r are 2.5 inches. angle x y z is 36 degrees. the length of side x y is 1.4 inches. what is the perimeter of δyxz? 3.5 in. 5.3 in. 6.4 in. 7.8 in.

6.4 inches

Step-by-step explanation:

See figure attached.

The perimeter of a triangle is obtained adding the length of all its sides. If the two triangles are congruent, then, all of they sides and angles are equal. Therefore QR = XY = 1.4 inches and PQ = PR = XZ = YZ = 2.5 inches. So, perimeter = QR + PQ + PR = 1.4 + 2.5 + 2.5 = 6.4 inches.

what is the original number? you forgot to add it.

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°