Two angles of a quadrilateral are 72 degrees and 56 degrees respectively and the remaining two angles are in the ratio 3:5. Find the measure of each angle of the quadrilateral.
Question
Two angles of a quadrilateral are 72° and 56° respectively and the remaining two angles are in the ratio 3:5. Find the measure of each angle of the quadrilateral.
✨ Free AI Tools for You
Powered by Chatterbot AI
Answer
Given:
- First angle: $72^\circ$
- Second angle: $56^\circ$
- Remaining angles: In the ratio $3:5$
Let the two remaining angles be $3x$ and $5x$.
According to the angle sum property of a quadrilateral: $$ 72^\circ + 56^\circ + 3x + 5x = 360^\circ $$
Combining the terms, we get: $$ 128^\circ + 8x = 360^\circ $$
Isolating $8x$: $$ 8x = 360^\circ - 128^\circ $$ $$ 8x = 232^\circ $$
Solving for $x$: $$ x = \frac{232^\circ}{8} $$ $$ x = 29^\circ $$
Now, we can find the measure of the remaining angles:
- Third angle: $3x = 3 \times 29^\circ = 87^\circ$
- Fourth angle: $5x = 5 \times 29^\circ = 145^\circ$
So, the measures of the angles of the quadrilateral are:
- First angle: $72^\circ$
- Second angle: $56^\circ$
- Third angle: $87^\circ$
- Fourth angle: $145^\circ$
India's 1^{st} AI Doubt Solver for CBSE, JEE, and NEET
Ask a Question for Freeand then it's just ₹212 a month