The answer is: m∡ KTL = 66°
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Given: m∡3 = m∡4 = 123° ;
Since the sum of ALL ANGLES in ANY TRIANGLE equal 180°;
→ the m∡ KTL = 180 − ( m∡ KLT + m∡TKL)
We want to find
1) m∡ KLT ; AND:
2) m∡ TKL ,'
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{Note: Alternatively, "m∡ KLT" can be written as: "m∡ TLK" ; and:
"m∡ TKL" can be written as: "m∡ LKT" . }.
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Since the sum of ALL ANGLES in ANY TRIANGLE equal 180;
→ m∡ KTL = 180 − ( m∡ KLT + m∡TKL) ;
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Or: → m∡ KTL = 180 − m∡ KLT − m∡TKL ;
Since, the distributive property of multiplication states:
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→ a* (b + c) = ab + ac ; AND
→ a *(b − c) = ab − ac
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Thus: m∡ KTL = 180 − ( m∡ KLT + m∡TKL) =
→ 180 − 1( m∡ KLT + m∡TKL ) ;
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→Note: The invisible "1" is implied, since anything multiplied by "1" equals that same value. We treat this as "-1" (negative one), due to the "minus sign).
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→ -1 * ( m∡ KLT + m∡ TKL ) =
→ -1 * (1 m∡ KLT + 1 m∡TKL ) =
→ (-1 * 1 m∡ KLT) + ( -1 * 1 m∡TKL ) =
→ (-1 m∡ KLT) + ( -1 m∡TKL) =
→ -1 m∡ KLT − 1 m∡TKL ;
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Now, bring down the "180" and rewrite:
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→ 180 − 1 m∡ KLT − 1 m∡TKL ; → Delete the "ones" ; and Rewrite:
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→ 180 − m∡ KLT − m∡TKL ;
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→ m∡ KTL = 180 − m∡ KLT − m∡TKL = 180 − (m∡ KLT + m∡TKL) ;
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→Now, solve for: m∡ KLT ;
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→Using the diagram; m∡ KLT = 180 − m∡4 ; Given m∡4 = 123; and
∡4 and ∡KLT are supplementary angles [the only two (2) angles on a particular straight line]; the sum of m∡4 and m∡KLT = 180.
→ m∡ KLT = 180 − m∡4 = 180 − 123 = 57 .
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→Now, solve for: m∡TKL ;
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→Using the diagram; m∡ TKL = 180 − m∡3 ; Given m∡3 = 123; and
∡3 and ∡TKL are supplementary angles [the only two (2) angles on a particular straight line]; the sum of m∡3 and m∡KLT = 180.
→ m∡ KLT = 180 − m∡4 = 180 − 123 = 57
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→So, in our "triangle": ΔKTL; we want to find the m∡T; that is m∡KTL;
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We know that each of the other 2 (two) angles in this triangles measures 57° .
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So, we calculate as follows:
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Method 1:
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m∡ KTL = 180 − ( m∡ KLT + m∡TKL)
= 180 − ( 57 + 57) = 66° .
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Or: Method 2:
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m∡ KTL = 180 − ( m∡ KLT + m∡TKL)
= 180 − ( 57 + 57)
= 180 − (57 * 2) = 180 − 114 = 66° .
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Or: Method 3:
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→ m∡ KTL = 180 − m∡ KLT − m∡TKL
= 180 − 57 − 57 = 66° .
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Answer: m∡ KTL = 66° .
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→ Let us check our answer to see if it "makes sense":
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66 + 57 + 57 =? 180?
66 + 57 = 123; 123 + 57 =? 180 ? Yes!
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