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One angle of a triangle measures $110^\circ$ . The other two angles are in a ratio of $2:5$ . What are the measures of those two angles? _\degree and _\degree

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Find missing angles in triangles using ratios

Full solution

Q. One angle of a triangle measures

110^\circ

. The other two angles are in a ratio of

2:5

. What are the measures of those two angles? _____\degree and _____\degree

Calculate Sum: Step $1$ : Calculate the sum of the remaining two angles. $\newline$ Since the sum of angles in a triangle is $180°$ , subtract the given angle from this total. $\newline$ Calculation: $180° - 110° = 70°$
Set Up Ratio: Step $2$ : Set up the ratio for the remaining angles. $\newline$ Let the measures of the two angles be $2x$ and $5x$ respectively.
Solve for x: Step $3$ : Solve for x using the equation from the sum of these angles. $\newline$ Equation: $2x + 5x = 70^\circ$ $\newline$ Calculation: $7x = 70^\circ$ $\newline$ $x = 70^\circ / 7$ $\newline$ $x = 10^\circ$
Calculate Angles: Step $4$ : Calculate the measures of the two angles using the value of $x$ . $\newline$ Angle $1$ = $2x = 2 \times 10^\circ = 20^\circ$ $\newline$ Angle $2$ = $5x = 5 \times 10^\circ = 50^\circ$

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