Question

A. If m<7 = 37 , what is in m<4 ?

b. If m<7 = 37 , what is in m<2 ?
c. Describe the relationship between <4 and <8 .
d. Describe the relationship between <3 and <5 .

Answer 1

a. if m<7 = 37, m<4 = 180 - 37 = 143
b. If m<7 = 37 , m<2 = m<7 = 37
c. m<4 = m<8 : corresponding angles
d. m<3 and m<5 are supplementary angles (m<3 + m<5 = 180)

Answer 2

a). m∠4 = 143°

b). m∠2 = 37°

c). ∠4 ≅ ∠8

d). ∠3 + ∠5 ≅ 180°

Explanation:

a). Given m∠7 = 37°

Since m∠7 ≅ m∠6 [Vertically opposite angles]

and m∠6 + m∠4 = 180° [Sum of interior angles formed by parallel lines l, m and transverse.]

Therefore, 37°+ m∠4 = 180°

m∠4 = 180 - 37

= 143°

b). Since m∠6 ≅ m∠2 [Corresponding angles]

and m∠6 ≅ m∠7 [Vertically opposite angles]

Therefore, m∠2 ≅ m∠6 ≅ m∠7 ≅ 37°

c). ∠4 ≅ ∠8 [Corresponding angles]

d). ∠3 + ∠5 ≅ 180° [Interior angles of parallel lines m, l and a transverse].