How would I set up my equation for letter b and c?

Question

asked Apr 18, 2023 116k views

1 Answer

Mahfuz Ahmed · Answer 1 · 2023-04-21T21:42:47+0000

d) Recall that by the exterior angle theorem we know that:

$a+b=d\text{.}$

Therefore,

$5x+10+6x+2=12x\text{.}$

Adding like terms we get:

$11x+12=12x\text{.}$

Subtracting 11x from both sides of the equation we get:

$\begin{gathered} 11x+12-11x=12x-11x, \\ 12=12x-11x, \\ x=12. \end{gathered}$

Therefore, we get that:

Recall that c and d are a linear pair, meaning:

$\measuredangle c+\measuredangle d=180^(\circ).$

Substituting d= 180 degrees and solving for angle c we get:

$\measuredangle c=180^(\circ)-144^(\circ)=36^(\circ).$

Answer part d):

$\begin{gathered} x=12, \\ \measuredangle c=36^(\circ). \end{gathered}$

c) To solve this question we will use the fact that the interior angles of a triangle add up to 180 degrees, and that h and i are a linear pair.

Since the interior angles of a triangle add up to 180 degrees, then:

$\measuredangle k+\measuredangle j+\measuredangle h=180^(\circ).$

Solving the above equation for angle h we get:

$\measuredangle h=180^(\circ)-\measuredangle j-\measuredangle k.$

Substituting ∡j=42°, ∡k=50° we get:

$\measuredangle h=88^(\circ).$

Now, since angles h and i are a linear pair, then:

$\measuredangle h+\measuredangle i=180^(\circ).$

Solving for angle i we get:

$\measuredangle i=180^(\circ)-\measuredangle h=180^(\circ)-88^(\circ)=92^(\circ).^{}$

Finally, we know that:

$\measuredangle i+\measuredangle n+\measuredangle m=180^(\circ).$

Substituting the measures of angles i, and n, and solving for m we get:

$\measuredangle m=180^(\circ)-92^(\circ)-33^(\circ)=55^(\circ).^{}$

Answer part c):