In a survey, a group of students were asked to name their favorite subject. There were 20 students who chose "other" subjects. H
1 answer:
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Answer:
10 cm
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = × d₁ × d₂ ( d₁ and d₂ are the diagonals )
Here A = 60, d₁ = 12, thus
60 = 0.5 × 12 × d₂ = 6 d₂ ( divide both sides by 6 )
d₂ = 10
The other diagonal is 10 cm
Answer:
Step-by-step explanation:
The opposite angles in a quadrilateral theorem states that when a quadrilateral is inscribed in a circle, the angles that are opposite each other are supplementary, their degree measures add up to 180 degrees. One can apply this here by using the sum of (<C) and (<A) to find the measure of the parameter (z). Then one can substitute in the value of (z) to find the measure of (<B). Finally, one can use the opposite angles in a quadrilateral theorem to find the measure of angle (<D) by using the sum of (<B) and (D).
Use the opposite angles in an inscribed quadrialteral theorem,
<A + <C = 180
Substitute,
14x - 7 + 8z = 180
Simplify,
22z - 7 = 180
Inverse operations,
22z = 187
z =
Simplify,
z =
Now substitute the value of (z) into the expression given for the measure of angle (<B)
<B = 10z
<B = 10()
Simplify,
<B = 85
Use the opposite angles in an inscribed quadrilateral theorem to find the measure of (<D)
<B + <D = 180
Substitute,
85 + <D = 180
Inverse operations,
<D = 95