91Ó°ÊÓ

If the two sides of a triangle are congruent then the angles opposite to those sides are congruent.

Consider $\mathrm{Δ}BDC$, in which$BDâ‰\dots DC$ then by isosceles triangle theorem, $∠1â‰\dots ∠2$, that is

$m∠1=m∠2=20$.

The measure of exterior angle is equal to the sum of measure of two remote interior angles of a triangle.

From the given figure, it can be observed that is$∠3$ exterior angle and$∠1\text{and}∠\text{2}$ are remote exterior angles, such that,

$$\begin{gathered} m∠3=m∠1+m∠2 \\ =20+20 \\ =40 \end{gathered}$$

Consider $\mathrm{Δ}ABD$, in which$ABâ‰\dots BD$ then by isosceles triangle theorem, $∠4â‰\dots ∠3$, that is,

$m∠4=m∠3=40$.

From the given figure, it can be observed that$∠5$ is exterior angle and$∠4\text{and}∠1$ are remote exterior angles, such that,

$$\begin{gathered} m∠5=m∠1+m∠4 \\ =20+40 \\ =60 \end{gathered}$$

Therefore, the measures of$∠3,∠4\text{and}∠\text{5}$ are$40,40\text{and60}$ respectively.

If the two sides of a triangle are congruent then the angles opposite to those sides are congruent.

Consider $\mathrm{Δ}BDC$, in which$BDâ‰\dots DC$ then by isosceles triangle theorem, $∠1â‰\dots ∠2$, that is

$m∠1=m∠2=x$.

The measure of exterior angle is equal to the sum of measure of two remote interior angles of a triangle.

From the given figure, it can be observed that $∠3$is exterior angle and $∠1\text{and}∠\text{2}$are remote exterior angles, such that,

$$\begin{gathered} m∠3=m∠1+m∠2 \\ =x+x \\ =2x \end{gathered}$$

Consider $\mathrm{Δ}ABD$, in which$ABâ‰\dots BD$ then by isosceles triangle theorem, $∠4â‰\dots ∠3$, that is,

$m∠4=m∠3=2x$.

From the given figure, it can be observed that $∠5$is exterior angle and $∠4\text{and}∠1$are remote exterior angles, such that,

$$\begin{gathered} m∠5=m∠1+m∠4 \\ =x+2x \\ =3x \end{gathered}$$

Therefore, the measures of$∠3,∠4\text{and}∠\text{5}$ are$2x,2x\text{and3x}$ respectively.