<A and <J are complementary angles. Find the value of x m<A = 5x + 30 m<J = 4x +15
1 answer:
Sum of complementary angles always equal to 90°.
Given, <A and <J are complementary angles. So, we can set up an equation as following:
m<A+ M<J= 90
Next step is to plug in m<A = 5x + 30 and m<J = 4x +15 in the above equation. So we will get,
5x+30+4x+15=90
(5x+4x)+(30+15)=90 Group the like terms.
9x+45=90 Combine the like terms.
9x+45-45=90-45 Subtract 45 from each sides.
9x=45 By simplifying.
Divide each sides by 9.
x=5.
So, x=5.
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Answer:
Givens:
Using this information we could recur to SAS postulate to demonstrate the congruence of this pair of triangles. We already have one side and one angle congruent, we just need to demonstrate that , that will prove the complete congruence.
So, based on the given coordinates, we're able to calculate the length of each side and find if they are the same. We use this formula:
Therefore, , because they have the same length.
Now, based on these congruences:
We demonstrate by the Side-Angle-Side (SAS) postulate that ΔABC ≅ ΔDEF.