Given m<6=142 find the measure of each missing angle, give your reasoning

Answer/Step-by-step explanation:

a. m<1 and m<6 are vertical angles, hence they are congruent.

Therefore, m<1 = m<6 = 142°

b. <2 and <6 form a linear pair.

Therefore, m<2 + m<6 = 180°

m<2 = 180° - 142° = 38°

c. <2 and <3 are interior angles of the same side of the transversal line, thus, they are supplementary.

Therefore:

m<2 + m<3 = 180°

m<3 = 180° - 38° = 142°

d. m<4 = m<2 = 38° (corresponding angles lying on the same side of the transversal line are equal)

e. m<5 = m<2 = 38° (vertical angles are equal)

f. m<7 = m<4 = 38° (vertical angles are equal)

g. m<8 = m<3 = 142° (vertical angles are equal)

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24