Find the measures of:all angles if 3(m∠1+m∠3) = m∠2+m∠4
Accepted Solution
A:
Answer:Part 1) m∠1=45°Part 2) m∠3=45°Part 3) m∠2=135°Part 4) m∠4=135°Step-by-step explanation:we know thatm∠1=m∠3 -----> by vertical angles Equation Am∠2=m∠4 -----> by vertical angles Equation Bm∠1+m∠2=180° ----> by supplementary angles (linear pair) Equation C3(m∠1+m∠3) = m∠2+m∠4 ----> Equation DSubstitute equation A and equation B in equation D3(m∠1+m∠1) = m∠2+m∠26(m∠1) = 2m∠23(m∠1) =m∠2 -----> equation ESubstitute equation E in equation C and solve for m∠1m∠1+3(m∠1)=180°4(m∠1)=180°m∠1=45°Find the measure of m∠3Remember thatm∠1=m∠3 (equation A)thereforem∠3=45°Find the measure of m∠2Remember thatm∠2=3(m∠1) (equation E)substitute the value of m∠1m∠2=3(45°)=135°Find the measure of m∠4Remember thatm∠2=m∠4 (equation B)thereforem∠4=135°