Question

Use the diagram to find the measures of all the angles, given that m<1 = 76º.

Answer 1

m<2 = 104º

m<3 = 76º

m<4 = 104º

Explanation:

given: m<1 = 76º

m<3 = m<1 this is because they are opposite angles which equals each other

A straight line = 180º

so m<1 + m<2 = 180 and m<3 + m<4 = 180

m<2 = 180 - m<1

m<2 = 180 - 76

m<2 = 104º

m<2 = m<4 so m<4 is also 104º

Hope this helps, Let me know if you have any questions !

Answer 2

m∠1 = 76° Given.

m∠1 ≅ m∠3 Vertical Angle theorem.

m∠3 = 76° CPCTC

m∠1 + m∠2 = 180° (supplementary angles)

m∠3 + m∠2 = 180° (supplementary angles)

m∠1 & m∠3 ∴ Congruent (congruent supplements theorem)

m∠2 + m∠3 = 180° (supplementary angles)

m∠4 + m∠3 = 180° (supplementary angles)

m∠2 & m∠4 ∴ Congruent (congruent supplements theorem)

∴ IF m∠1 = 76° (Given)

THEN:

m∠2 = 104° (Supplementary angles)

m∠3 = 76° (Definition of vertical angles)

m∠4 = 104° (Supplementary angles)