If Delta ABC sim Delta PQR for the correspond | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the ratio of the angles in $\Delta ABC$ is $m \angle A : m \angle B : m \angle C = 2 : 3 : 5$.Let the angles be $2x, 3x,$ and $5x$.Since the

Vedclass · Accepted Answer

$54$

Vedclass · Answer

(B) Given the ratio of the angles in $\Delta ABC$ is $m \angle A : m \angle B : m \angle C = 2 : 3 : 5$.Let the angles be $2x, 3x,$ and $5x$.Since the sum of angles in a triangle is $180^{\circ}$,we have $2x + 3x + 5x = 180^{\circ}$.$10x = 180^{\circ} \implies x = 18^{\circ}$.Therefore,$m \angle A = 2(18^{\circ}) = 36^{\circ}$,$m \angle B = 3(18^{\circ}) = 54^{\circ}$,and $m \angle C = 5(18^{\circ}) = 90^{\circ}$.Given the similarity correspondence $ABC \leftrightarrow QRP$,the corresponding angles are equal.Thus,$m \angle A = m \angle Q$,$m \angle B = m \angle R$,and $m \angle C = m \angle P$.Since $m \angle B = 54^{\circ}$,it follows that $m \angle R = 54^{\circ}$.

If $\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow QRP$ and $m \angle A : m \angle B : m \angle C = 2 : 3 : 5$,then $m \angle R = \dots$ (in $^{\circ}$)

Similar Questions

Given $\Delta PQR \sim \Delta XYZ$ for the correspondence $PQR \leftrightarrow XYZ$. If $\frac{PQ}{3} = \frac{XY}{5}$ and $QR = 9$,find the length of $YZ$.

In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AM}$ is an altitude. If $AM = 15$ and the perimeter of $\Delta ABC$ is $50$,find the area of $\Delta ABC$.

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $YM = 12$ and $XM = 8$,find $XZ$.

In the figure,$PA$,$QB$,$RC$,and $SD$ are all perpendiculars to a line $l$. Given $AB = 6 \, cm$,$BC = 9 \, cm$,$CD = 12 \, cm$,and $PS = 36 \, cm$. Find $PQ$,$QR$,and $RS$.

In the figure,if $\angle A = \angle C$,$AB = 6 \, cm$,$BP = 15 \, cm$,$AP = 12 \, cm$,and $CP = 4 \, cm$,then find the lengths of $PD$ and $CD$ (in $cm$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module