Question

The measures of angles of a triangle ABC, ∠A:∠B:∠C are in the ratio of 5:2:3 respectively. Find the measures of ∠A.

a) 90 degree
b) 36 degree
c) 54 degree
d) 60 degree​

Answer 1

∠A:∠B:∠C= 5:2:3

∠A=5$x$

∠B=2$x$

∠C=3$x$

Sum of measure of angles in a triangle= 180°

5$x$ + 2$x$ + 3$x$ = 180°

10$x$ = 180°

$x$ = $\frac{180}{10}$= 18

∠A=5$x$=5x18=90°

∠B=2$x$=2x18=36°

∠C=3$x$=3x18=54°

Thus, Angle A= option a. 90 degrees.

Answer 2

The measures of angles of a Δ ABC, ∠A:∠B:∠C are in the ratio of 5:2:3.

let, the common ratio b/w them be x

$\therefore \: \angle \: a \ratio\angle \: b\ratio\angle \: c = 5x\ratio2x\ratio3x \\ \\ we \: know \\ sum \: ofmeasures \: of \: all \: angles \: in \: triangle \: = 180 \degree \\ \\ \angle \: a + \angle \: b +\angle \: c = 180 \degree \\ \therefore5x + 2x + 3x = 180 \\ 1 \cancel{0}x = 18 \cancel{0} \\ x = 18 \\ \\ \underline{\boxed{\sf{ measure s\: of \: \angle \: a = 5x = 90 \degree}}}$