Single Choice

In $$\triangle ABC$$, side $$BC$$ has been produced to $$D$$. If $$\angle BAC$$ = $$45^{o}$$ and $$\angle ABC$$ = $$55^{o}$$, then $$\angle ACD$$ = ?

A$$80^{o}$$
B$$90^{o}$$
C$$100^{o}$$
Correct Answer
D$$110^{o}$$

Solution

(c) $$100^{o}$$
Because,
We know that the exterior angle of a triangle is equal to the sum of its interior opposite angles.
$$\therefore \angle ABC + \angle BAC$$ = $$\angle ACD$$
= $$55^{o} + 45^{o}$$ = $$\angle ACD$$
= $$\angle ACD$$ = $$100^{o}$$

SIMILAR QUESTIONS

Lines and Triangles

In $$\triangle ABC$$, side $$BC$$ has produced to $$D$$. If $$\angle ACD$$ = $$132^{o}$$ and $$\angle BAC$$ = $$54^{o}$$, then $$\angle ABC$$ = ?

Lines and Triangles

In the given figure, side $$BC$$ of $$\triangle ABC$$ is produced to $$D$$ such that $$\angle ABC$$ = $$70^{o}$$ and $$\angle ACD$$ = $$120^{o}$$. Then, $$\angle BAC$$ = ?

Lines and Triangles

In the given figure, $$\angle A$$ = $$50^{o}$$, $$CE \parallel BA$$ and $$\angle ECD$$ = $$60^{o}$$. Then, $$\angle ACB$$ = ?

Lines and Triangles

In the figure given alongside, find the measure of $$\angle ACD$$

Lines and Triangles

In the figure given alongside, find the values of $$x$$ and $$y$$

Lines and Triangles

In the figure given alongside, find the values of $$x$$ and $$y$$

Lines and Triangles

An exterior angle of a triangle measures $${110}^{o}$$ and its interior opposite angles are in the ratio $$2:3$$. Find the angles of the triangle.

Lines and Triangles

In the figure, $$ \angle B=65^o $$ and $$ \angle C = 45^o $$ in $$ \triangle ABC $$ and $$ DAE \parallel BC $$. If $$ \angle DAB = x^o $$ and $$ \angle EAC = y^o $$, find the values of x and y.

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