see how it do it in the picture and hope it helps you..
David rolls a fair dice 240 times. How many times would David expect to roll a three?
1 answer:
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Answer:
Part 1)
Part 2)
Part 3) m∠K=61°
Part 4) m∠L=119°
Part 5) m∠M=61°
Step-by-step explanation:
we know that
In a parallelogram opposite angles and opposite sides are congruent and consecutive angles are supplementary
Part 1) Find the side MN
we know that
MN≅KL ----> by opposite sides
we have
therefore
Part 2) Find the side KN
we know that
KN≅LM ----> by opposite sides
we have
therefore
Part 3) Find the measure of angle K
we know that
m∠K+m∠N=180° ----> by consecutive interior angles
we have
m∠N=119°
substitute
m∠K+119°=180°
m∠K=180°-119°
m∠K=61°
Part 4) Find the measure of angle L
we know that
m∠L≅m∠N ----> by opposite angles
we have
m∠N=119°
therefore
m∠L=119°
Part 5) Find the measure of angle M
we know that
m∠M≅m∠K ----> by opposite angles
we have
m∠K=61°
therefore
m∠M=61°
<u>Given</u>:
Line m is parallel to line n.
The measure of ∠1 is (4x + 15)°
The measure of ∠2 is (9x + 35)°
We need to determine the measure of ∠1
<u>Value of x:</u>
From the figure, it is obvious that ∠1 and ∠2 are linear pairs.
Thus, we have;
Substituting the measures of ∠1 and ∠2, we get;
Thus, the value of x is 10.
<u>Measure of ∠1:</u>
The measure of ∠1 can be determined by substituting x = 10 in the measure of ∠1
Thus, we have;
Thus, the measure of ∠1 is 55°