Question

If the ratio of angles in a triangle is 3:4:5 then find the measures of angles in the triangle.

• A. 45${}^{\circ }$, 60${}^{\circ }$, 95${}^{\circ }$
• B. 30${}^{\circ }$, 60${}^{\circ }$, 75${}^{\circ }$
• C. 45${}^{\circ }$, 65${}^{\circ }$, 75${}^{\circ }$
• D. 45${}^{\circ }$, 60${}^{\circ }$, 75${}^{\circ }$

Answer 1

The correct option is D

45${}^{\circ }$, 60${}^{\circ }$, 75${}^{\circ }$

Given the ratio of angles in a triangle is 3:4:5

$\therefore$ Let the angles be 3$x$, 4$x$, 5$x$.

$\because$ Sum of angles in a triangle = 180${}^{\circ }$

$\Rightarrow$ 3$x$ + 4$x$ + 5$x$ = 180${}^{\circ }$

$\Rightarrow$ 12$x$ = 180${}^{\circ }$

$\Rightarrow$ $x$ = 15${}^{\circ }$

$\therefore$ The angles are 3$x$, 4$x$, 5$x$

= 3 $\times$ 15${}^{\circ }$, 4$\times$ 15${}^{\circ }$, 5$\times$ 15${}^{\circ }$

= 45${}^{\circ }$, 60${}^{\circ }$, 75${}^{\circ }$