Answers:
x = 5
m∠C = m∠H = 38 degrees
WORKINGS
Given that ABCD ≅ FGHJ
We know that corresponding angles of two congruent
quadrilaterals are equal
Therefore,
m∠A = m∠F
m∠B = m∠G
m∠C = m∠H
m∠D = m∠I
Given,
m∠C = 9x – 7
m∠H = 5x + 13
Since m∠C = m∠H
9x – 7 = 5x + 13
Add 7 to both sides of the equation
9x – 7 + 7 = 5x + 13 + 7
9x = 5x + 20
Subtract 5x from both sides of the equation
9x – 5x = 5x – 5x + 20
4x = 20
Divide both sides of the equation by 4
4x/4 = 20/4
x = 5
To determine the measures of angle C and angle H
m∠C = m∠H
We know that m∠C = 9x – 7
Since x = 5
m∠C = 9(5) – 7
m∠C = 45 – 7
m∠C = 38
Therefore, m∠C = m∠H = 38 degrees
Answer:
ΔRMS ≅ ΔRQS by AAS
Step-by-step explanation:
See the diagram attached.
Given that ∠ RMS = ∠ RQS and N is any point on RS and ∠ MRS = ∠ SRQ.
Therefore, between Δ RMS and Δ RQS, we have
(i) ∠ RMS = ∠ RQS {Given}
(ii) ∠ MRS = ∠ SRQ {Also given} and
(iii) RS is the common side.
So, by angle-angle-side i.e. AAS criteria we can write ΔRMS ≅ ΔRQS. (Answer)
Answer:
The age of mother is:
40 years
Step-by-step explanation:
2a = 5b
b = 16
a = age of a mother
b = age of her son
2a = 5*16
2a = 80
a = 80/2
a = 40
probe:
2*40 = 5*16 = 80
Answer:
$578.30
Step-by-step explanation:
537.95(.075)= 40.35
$40.35 + $537.95 = $578.30
