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& find measure
/_1=/_2
of 2
19. 21 and
/_2 are vertical angles. If
m

/_1=(7x-10)^(@) and
m/_2=(5x+12)^(@), then find the measure of
/_2.

\& find measure $\angle 1=\angle 2$ $\newline$ of $2$ $\newline$ $19$ . $21$ and $\angle 2$ are vertical angles. If $m$ $\newline$ $\angle 1=(7 x-10)^{\circ}$ and $\mathrm{m} \angle 2=(5 x+12)^{\circ}$ , then find the measure of $\angle 2$ .

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Find equations of tangent lines using limits

Full solution

Q. \& find measure

\angle 1=\angle 2

\newline

of

2

\newline

19

.

21

and

\angle 2

are vertical angles. If

m

\newline

\angle 1=(7 x-10)^{\circ}

and

\mathrm{m} \angle 2=(5 x+12)^{\circ}

, then find the measure of

\angle 2

.

Vertical Angles Equality: Since angle $1$ and angle $2$ are vertical angles, they are equal. $m/_{1} = m/_{2}$
Plug in Expressions: Plug in the expressions for $m/_{1}$ and $m/_{2}$ . $\newline$ $(7x - 10) = (5x + 12)$
Solve for x: Solve for x. $\newline$ $7x - 10 = 5x + 12$ $\newline$ $7x - 5x = 12 + 10$ $\newline$ $2x = 22$ $\newline$ $x = 11$
Substitute $x$ into $m/_{2}$ : Now, substitute $x$ back into the expression for $m/_{2}$ .
$m/_{2} = (5x + 12)$
$m/_{2} = (5\cdot 11 + 12)$
$m/_{2} = (55 + 12)$
$m/_{2} = 67$ degrees

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