$\dfrac{2m}{5}+3=7(4m-3)\ \ \ \ |use\ distributive\ property:a(b-c)=ab-ac\\\\\dfrac{2m}{5}+3=28m-21\ \ \ \ \ |multiply\ both\ sides\ by\ 5\\\\2m+15=140m-105\ \ \ \ |subtract\ 140m\ from\ both\ sides\\\\-138m+15=-105\ \ \ \ |subtract\ 15\ from\ both\ sides\\\\-138m=-120\ \ \ \ |divide\ both\ sides\ by\ (-138)\\\\m=\dfrac{120:6}{138:6}\\\\\boxed{m=\frac{20}{23}}$

7 0

3 years ago

Finding angle measure using triangles

Rainbow [258]

x = 58°

Explanation:

According to the diagram, lines HI and JK are parallel to each other.

∠AHI = 60°

∠JKI = 62°

∠JKI and ∠HIA are equal because when two lines are parallel then the corresponding angles are equal.

So,

∠JKI = ∠HIA = 62°

In ΔHIA,

∠AHI + ∠HIA + ∠IAH = 180°

60° + 62°+ x = 180°

122° + x = 180°

x = 180° - 122°

x = 58°

3 0

4 years ago